Wendy Cope's life is largely absurd to her. The 55-year-old is a poet - "a poet", she says, staring out of her publisher's office window with a mixture of amusement and alarm. "I would be less surprised if I were, say, writing children's stories." Her third volume of poetry, If I Don't Know, comes out next month and Cope is measuring herself against the expectations she had 35 years ago as a miserable student at Oxford. "I always knew I could write. But the idea that I would ever publish a poem I find surprising. When I was at school poetry was so boring. It was all about nature, all set in the countryside, and I grew up in a suburb, so it didn't seem to have much to do with me."

Unless it is being parodied, the countryside doesn't feature much in Cope's work, which is about loss and abandonment and getting a raw deal out of love, although in a humorous rather than a drippy way, which is why it has attracted the label "light verse" and she "man-hater". She has been compared, somewhat bitchily for both parties, to Pam Ayres, the relentlessly twee author of such standards as "The Bunny Poem" and "The Hair curlers Poem", and was once put on the national curriculum as recommended reading for 12-15-year-olds. "I thought, yes," she says, with mild annoyance "that is because they think I am easy."

It irks because Cope's life has not been easy, running on loneliness and depression and an anxiety which, although she is more content these days, reveals itself in a certain over-scrupulous primness of manner. Being interviewed, she seems suspended on the threshold of an awkward silence. In her poem "How to Deal with the Press" she writes, "She'll urge you to confide. Resist./Be careful, courteous and cool./Never trust a journalist."

Andrew Motion, the poet laureate describes her as "a person of rather impressive seriousness". He has been a champion of Cope's work since first publication. "She is high-minded without being pompous, a mixture of the same sort of things you get in her poetry."

"Her sense of fun is rather wry," says Craig Raine, the poet and one of Cope's first editors. "She's a great teaser. She's got a very lively eye for absurdity." When her first volume, Making Cocoa For Kingsley Amis, was published in 1986, it sold 40,000 copies, a massive bestseller by poetry standards (Seamus Heaney's Beowulf, by comparison, sold some 34,000). Most of the poems rhymed, and if you skimmed their titles appeared to be about things like lavatory attendants, budgerigars and giving up smoking. They were very funny. In "My Lover" she observed: "At the age of 49 he can make the noise of five different kinds of lorry changing gear on a hill." She parodied the voices of William Wordsworth, Ted Hughes and, most memorably, TS Eliot, who in Waste Land Limericks, was boiled down to the stanza: "No Water. Dry rocks and dry throats,
Then thunder, a shower of quotes
From the Sanskrit and Dante.
Da. Damyata. Shantih.
I hope you'll make sense of the notes."

She created the hilarious male alter ego, Jason Strugnell, an intolerable egotist who wrote odes to his neighbour's cherry blossom tree and used words like "senescent" and "beauteous", establishing Cope's contempt for a certain kind of tedious male poet.

Beneath the jollity, however, there was something unsettling about Cope's poems that made her, a former schoolteacher, unsure of their suitability for young readers. What, for example, was a 12-year-old to make of the poem "At 3 am", about waking up in the middle of the night beside a man whose sleep she didn't want to disturb with her crying? Or the observation in "After Prague", a poem about suicide, "Hope is a long leash/Drawn in slowly"? Or, in "Defining the Problem", the lover's paradox, "I cannot cure myself of love/For what I thought you were before I knew you," all forecasts of adult life which seemed rather too alarming for a year eight English class.

The depth and pathos of Cope's poems have always been obscured by her wit, a trade-off that maddens her, since a lot of her work has been motivated by - and seeks to articulate - total despair. For 14 years, she lived in south London and taught in a state primary school in the Old Kent Road where, despite interludes of happiness, she was desperately lonely and couldn't shake the feeling that there was something else she should be doing.

"I wasn't convinced that teaching was the career for me. In those days, you really had to be good at art and craft and I was never very practical. I always said that the ideal primary school teacher was a bloke who likes football and wants to build his own rabbit hutch." What she does owe teaching, she says, is the gift of alerting her to her own creativity, and by boring her so much in the latter years, forcing her to do something about it. "It brought out things I might not otherwise have discovered, because it was in an era when there was a lot of emphasis on creativity. Before then I had tended to think of myself as a brainy person who wasn't very creative."

When Cope's first book came out, she was welcomed by critics as an original voice, an "observer of pomposity," wrote Alison Coles in the Guardian, "from whom even the most serious subjects are not immune from irreverent treatment". Still, there was something in her tone that the critics found obnoxious and a note of condescension crept into reviews that implied she was squandering her talent on trivia. "She is witty and unpretentious, which is both her strength and her limitation," wrote Robert O'Brien in the Spectator, an assessment that so infuriated Cope she dashed off a reply called "Serious Concerns", which gave her the title for her second volume:

"I'm going to try and overcome my limitation -
Away with sloth!
Now should I work at being less witty? Or more pretentious?
Or both?"

Serious Concerns, although bleaker in outlook than Cocoa, was made equally light of. "A dozen or so squiblets about cats or alcohol or washing-up, tiny insights that hardly justify having a page to themselves," complained John Walsh in the Independent. And yet, there were other readers who detected something fierce and devastating in Cope's work which aligned her more aptly with Stevie Smith. "What's funny about her is very difficult to separate from what's serious about her," says Andrew Motion.

"I think of her as a - I don't quite want to say Mrs Prufrock, but sort of Prufrock's sister, with that world-weary, disillusioned self-mockery and the feeling of being trapped. In her early work, the comedy is more obviously in the foreground, but even in the Strugnell poems, you get a portrait of a man who is in all senses of the word sad, which stops you in your tracks while you are laughing at him."

"She appeals to people who don't normally read poetry," says Carol Rumens, a fellow-poet. "And she seems to do so without compromising the art or the technique of it. I was at a reading with her in Birmingham once and she had crowds of people queueing up to have their books signed. It was quite daunting." Wendy Cope's new volume, out in a fortnight, is dedicated "To LM with love and thanks", a tip-off that indicates a shift in tone. Whereas Serious Concerns, not dedicated to anyone, opened nine years ago with the poem, "Bloody Men" ("Bloody men are like bloody buses -/You wait for about a year/And as soon as one approaches your stop/Two or three others appear"), If I Don't Know issues forth with the news flash, "Write it in fire across the night:/Some men are more or less all right." ("When I do that one at readings I say, 'this shows how much I've mellowed'," she says.)

For once in her life, Cope is in love and he isn't a bastard. LM, Lachlan Mackinnon, is a poet and author and for the last seven years the two have lived together in Winchester, an arrangement, says Cope, that has made her happier than she has ever been. "I was in my late 40s when I moved in with Lachlan. That might cheer up some younger women. I'd never really been happy before, so when I first moved in I felt worried that something would happen. But now that we've had seven years, I feel more relaxed. Seven years! when I was so afraid that something would go wrong after seven weeks or seven months! Not that we would go off each other, but that one of us would die." She checks herself, brusquely. "Yes, anyway."

Cope's efforts to capture the switchback nature of happiness are, believes Craig Raine, what makes If I Don't Know her best book to date. "There are a great many poems about being happy which have a tremendous note of sadness also, based on the knowledge that happiness will inevitably pass. The opening poem, "Round Pond", where she is watching herself watching herself, and doesn't know who's in charge of the plot, seems to me immensely subtle and plangent."

"When I first moved in," says Cope, "I would cry a lot. It would take almost nothing to make me cry - and I don't mean him upsetting me. I mean things on television. And I realised that there was a lot of sadness in me and in a way it was safe to let it come out."

Anxiety has been an almost constant presence in Cope's life since her parents, Fred and Alice, sent her to a Methodist boarding school - Farringtons School, Chiselhurst, in Kent,- at the age of seven. She was painfully well behaved. Her father, who worked alongside her mother as the manager of Mitchell's department store, in Erith, Kent, suffered from tuberculosis and the house had to be kept oppressively clean. It was not a place for running riot and any rebellious instincts were checked by the fear she might damage her father. Fred Cope died when his elder daughter was 26. "We've grown up struggling, frightened that the family would drown us," she wrote in "For My Sister, Emigrating", "Only giving in to love when someone's dead or gone."

Since both of Cope's parents left school at 14, they wanted their two daughters to have an expensive education. "They could afford to send me to a boarding school," says Cope, "although it wasn't a very good one. It's quite sad, because I would have had a better education at a grammar school and I did pass the 11-plus, but they thought they were doing the best thing."

The religious instruction was intense. Cope's grandmother was a baptist, her mother a Billy Graham fan and she had a great aunt in the British Women's Total Abstinence League in Hartlepool. "They were low-church Christians. My mother is very much of the English puritan tradition. When I got interested in the theatre as a teenager, she got quite funny. I knew she didn't like sex and things, but I didn't realise she disapproved of the theatre." Cope would later lampoon the evangelists in a series of poems called Strugnell's Christian Songs ("When I went out shopping,/I said a little prayer:/'Jesus, help me park the car/For you are everywhere.''")

Since both her parents worked, when Cope's younger sister was born her grandmother moved into the family home to help out. She taught Cope to read and is remembered in the poems "Names" and "Present", two of Cope's least cynical offerings. Cope says, "She was kind to us. She'd had a hard life. She was quite timid in some ways. She didn't go out a lot. She was good with figures. She had a horrible mother who was quite cruel to her. Nanna taught me the sounds of the alphabet, and then one day I was looking over her shoulder and realised I could read it myself. And - I feel awful about this - I grabbed the book and said I didn't want her to read to me any more. I feel awfully sad about that."

Cope was the first in her family to go to university. She won a place at Oxford to read history and once there, her anxieties mushroomed. She felt inadequate and preoccupied with failure. "I think there's a poem to be written entitled, My Intellectual Life at Oxford, and I think it would be a couplet. My Emotional Life at Oxford, however, that would be a novel. I had a difficult time. I was terrified of my tutors, these horrible women in St Hilda's. When I tell Oxford people who my tutors were, they say, 'oh you were unlucky'. When I got there I was warned that one of them would probably only like me if I was very pretty or very rich or if my father was someone famous. And another one was a dried up medievalist, very distinguished, wasted on me."

She didn't get into poetry. She didn't get into anything much, but she did rebel against religion after being asked, at a university Bible meeting, to pray for the Catholic nuns who were attached to her college, to see the error of their ways. That, she says, was the final straw and she remained estranged from the church for 30 years. It is only since moving to Winchester and finding herself five minutes walk from the cathedral, that she has tentatively resumed attendance, at first just to listen to the music, and then for other reasons.

"It was to hear the language of the prayer book, which was part of my childhood, and which I love," she says. "At the time when my last book was published I called myself an atheist. Those poems were taking the piss out of a certain kind of evangelical. I'm a bit embarrassed about them now. I mean the dean of Winchester said to me, I bought your book. But he was fine about it and told me that his daughter liked it too. And some church people have said they like those poems, but they're the sort of people who like traditional services, as I do."

Her mother, however, was not amused by Strugnell's Christian Songs, or the dissection of all those hideous relationships in Making Cocoa. Cope talks about her mother's disapproval with resignation, although a brittle tone creeps in. "I don't think she and my stepfather like my poems very much, actually," she says, carelessly. "But they enjoy it if someone hears me on the radio. I sometimes think they're proud of me, but I don't see much sign that they enjoy my work - although my stepfather loved Twiddling Your Thumbs, the book of children's poems, because he's very good with children."

She thinks for a moment. "There's a heartrending story about [the poet] Tony Harrison, whose first book had quite a lot of sex in it. He didn't give a copy to his parents, because he knew it would upset them, so his parents went and got it out of the public library. And I thought, yeah. What do you do? Do you give them a copy? So I've always given my mum the books." She pauses and examines the middle distance. "But in the past, my poems have been something of an embarrassment. So there's that as well."

It took Cope years to come to terms with this fear of embarrassment, a peace of mind achieved partly through analysis and partly through writing. When she started out in teaching, however, having trained at Westminster College, Oxford, she had no ambitions beyond keeping the class orderly. The first years were difficult ones of establishing authority. But the children made her laugh. "When I was a young teacher I didn't have a television set,'' she once recalled. "My pupils felt sorry for me. 'Miss,' said one kindly eight-year-old, 'if you got a job, you could save up and buy a telly.' I was so touched I didn't have the heart to explain that I had a job already.'' (She later became TV critic for the Spectator).

As she moved up the school ranks in south London, problems with her pupils gave way to problems in staff management. She became a deputy head teacher and ended up staying in the system for 14 years. Cope looks back on her teaching career as something she endured beyond the limits of toleration, but also something that she owes a great deal to. In the 70s, she was sent by the school on an Inner London Education Authority music course. As a good pianist, one of the best bits of her job was teaching music.

"The idea of this course was to get the children to create their own music, and to do it in an avant garde idiom, so that they didn't need to know about harmony. It was wonderful and I started thinking, I want to be a composer, but I also thought, I'm not really good enough at music to be a composer. Then I remembered that what I was good at was English, so why don't I try to do these creative things with words."

That is how it started. As she became more creatively aware, Cope went to see a Freudian analyst, Arthur S Couch, who she would visit on a weekly basis for 11 years and would dedicate Making Cocoa to. It was with Couch that she learnt how to "misbehave", to rewrite all those starchy codes of conduct that had been drummed into her in Erith. In her sessions with Couch she worked out all the aggression she'd been too frightened to direct at her parents. She had always, she says, been too good.

"There may have been times when [Couch] was genuinely worried that the analysis was becoming a bit too unconventional. Occasionally I threatened to do something really bad, like taking all my clothes off, or not paying the bill, but it never came to that. What did eventually emerge, along with the innocent mischief, was a lifetime of repressed aggression. In my adolescence I had been afraid to fight with my parents for fear of killing my elderly father. As I grew bolder, the poor old shrink copped the lot."

As Cope's confidence grew, so she began to chase her new interest in writing. Finding people to discuss poetry with was difficult: she approached old university friends who had studied English, but her request made them shuffle and look embarrassed. Eventually, she enrolled on an Arvon writing course and took evening classes at Goldsmiths' College, London. The reason she chose poetry over prose was its brevity - there was no time to get caught up in long novels. Her initial efforts were very serious, exercises in building self-esteem. But gradually she began to allow her sense of humour in.

"Beginning to write was very important. It was a question of realising that I had a right to my own view of things. I think often I'd allowed other people to impose on me their view of what was happening in my life. I also had difficulty - as other people who've been in psychotherapy do - in seeing things with my own eyes. I'd look at a beautiful landscape and think, what would Wordsworth have said about this? I had to realise that I had a right to see the world. It was like clearing a space where I was allowed to do that. The last thing I was thinking about was publishing poems."

The old anxieties are still there. When Wendy Cope writes a poem these days, she tries to maintain the illusion that it isn't for publication. After the Arvon course, she succeeded in getting a few poems published, and in 1984, feeling totally burnt out, quit teaching and took a part-time administrative job at London's county hall. Two years later Making Cocoa came out, and she left work altogether. The book's success left her dizzy - she recoiled from the publicity - and entered what would become the depressing years of isolation out of which Serious Concerns would grow.

"I thought that when I gave up work, the difficult thing would be anxiety about money. But actually, what I hadn't bargained for was that I was so lonely. I lived by myself in London and really missed having people I saw every day to talk to if the washing machine broke down."

She made the decision to do anything for money but write - radio shows, readings, public appearances - and to guard, in her head, a private space reserved for poetry. "The only way I can be fearless is by saying to myself, I'm not going to publish this, I just feel like writing a poem. I don't have to publish it or show it to anybody. They are sometimes my best poems. But I sometimes have to work myself into quite an aggressive state to be able to write. It may be one of the reasons that I write so little - to clear a space where I'm not going to be worrying about what anyone will think."

When Ted Hughes died, Cope's name was thrown into the ring as a potential laureate. The idea appalled her - all that pressure and attention - but with reflex good manners she desisted from joining the public debate in case it offended the people who had nominated her. What did excite her was coming top of a popular vote conducted by Radio 4. "I was pleased with that," she says. "Then when they wanted to talk to me I pretended that my agents couldn't get hold of me. After all these people voted for me, I couldn't very well go on the radio and say I didn't want it."

Cope is more relaxed now than she has ever been. Across the road from her house is a water meadow which Keats referred to in his letters of 1819 as a place he often walked through. It pleases Cope to think that one day, after returning from a walk there, he wrote "Ode to Autumn". She does the occasional reading at a secondary school, where the adolescents think it's a poet's job to tell off the world and find her awfully frivolous. Cope has come to the conclusion that growing up is a process of becoming more frivolous.

There are other resolutions. These days, she says, she wouldn't call herself an atheist, hinting at as much in the poems "The Christmas Life" and "Present", gentle admissions if not of faith then at least of the suspension of doubt. She can even look back fondly at teaching. Last Christmas, Cope passed a brass band in Winchester High Street as it was playing "Little Donkey", that staple of the primary school carol concert. To her amazement, she found tears in her eyes. "Who'd have thought I'd get nostalgic over 'Little Donkey?'"

And she takes a ruder approach to criticism. "Alan Bennett once said there should be a notice in the National Gallery saying 'you don't have to like everything here,' and I think that should be at the front of every anthology of poetry." You don't have to like everything - it is the hard-won lesson of her life.

Life at a glance: Wendy Mary Cope

Born: July 21 1945.

Educ: Farringtons School, Chiselhurst, Kent; MA (history) St Hilda's College, Oxford; Westminster College of Education, (DipEd).

Partner: Lachlan Mackinnon, poet and writer (1993-).

Career: Primary teacher, London (1967-81); administrator, county hall, London ('81-84); part-time teacher ('84-86); television critic, the Spectator ('86-90).

Publications: Making Cocoa For Kingsley Amis (1986); Twiddling Your Thumbs (rhymes for children, '88); The River Girl ('91); Serious Concerns ('92); If I Don't Know (2001).

Awards: Cholmondeley Award for Poetry, 1987; Michael Braude Award, American Academy of Arts and Letters, 1995.

• If I Don't Know is published by Faber on June 4.