Mark Heap is wryly recalling an online comment describing his bizarre turn in Channel 4's Green Wing. It ran: "Mark Heap doing his usual mad thing, but slightly fatter." "Which I thought was brilliant," he says, "but it's kind of true."

Heap has become television's go-to oddball, best known for the roles of otherworldly conceptual artist Brian in Spaced and Green Wing's outlandish and obsessive Dr Alan Statham. More recently, he's been stealing scenes in Friday Night Dinner as an over-friendly neighbour. Now he is returning to the stage after a 20-year hiatus. Next week he takes over from Matthew Macfadyen as PG Wodehouse's famously unflappable butler in the Jeeves and Wooster comedy Perfect Nonsense, alongside Peep Show star Robert Webb (replacing Stephen Mangan) as his foolhardy employer.

When we speak at the Duke of York's theatre in the West End, at the end of a long day of rehearsals, Heap confesses that throughout his years of TV work, he was rarely tempted by theatre roles. Jeeves, however, was a part he could not turn down. "It came along and I found it difficult, nigh-on impossible, to say no to."

It was the appeal of PG Wodehouse's fiction that clinched it. "It's just a joy to read," Heap says simply. "They make such a mountain out of nothing – there's high farce over a teapot or an ashtray." Heap also revels in Wodehouse's distinctive, elaborate use of language. "On the one hand you're saying a thousand words with two words, like 'indeed sir', or you're saying one word using 30 – it's brilliant. There's so much implied."

Heap was particularly impressed by the way Robert and David Goodale's stage adaptation manages to retain the memorable prose of Bertie Wooster's narration. The action is framed within a play put on by the protagonist – with only his aunt's servant Seppings, and Jeeves, to assist him. Cue chaos, confusion and quick changes. "There are two levels," says Heap. "The Wodehouse meat and the froth of watching people struggling to double up and play with all the theatrical conventions."

Does Wodehouse's distant world of buttoned-up butlers and fearsome aunts have anything to say to us today? Heap suggests that it is precisely because Wodehouse's characters are so of their time that they continue to tickle audiences, tapping into a very British brand of nostalgia. Unlike Shakespeare, whose works have been relocated to every era and setting imaginable, Wodehouse's stories demand to remain firmly in the early 20th century; any attempt to update them, Heap argues, "would be hopeless".

In person, Heap is unexpectedly straightforward – unassuming, almost – revealing only the occasional glimmer of the strangeness that animates his TV performances. Although he insists his succession of quirky roles was a "total accident", he admits that "arsing about and being silly" have always appealed to him as a performer. The Green Wing cast had two months together before getting in front of a camera – "you develop little tics". As for Brian: "he was meant to be quite flamboyant and I found myself, just because I was in the mood that day, thinking: what if he was really uncertain and a bit tortured. It built from there."

The business can narrow you down, Heap says. "You start off going, 'I can play anything', and slowly you get whittled down." But he shrugs at the happy coincidence of his career: "I've always just fuddled along. I do my job and it's all I'm any good at to be honest."

A year into university, he ran away from his studies – not with the circus, but with Fools Theatre, a touring company producing Pinter plays and "avant-garde, mime dance-movement things". From there, he joined his brother Carl's Medieval Players company, performing all around the world until he and fellow actor Mark Saban splintered off to form a street theatre duo, The Two Marks, which eventually led to television work.

Is it intimidating to return to theatre in a role with as rich a history as Jeeves? Heap concedes that the prospect is "bloody daunting", but adds: "like any character, you have to bring your own thing to it". He is still discovering his idiosyncratic take on the character, explaining that his approach tends to be "instinctive" rather than psychological. In a show that takes a sledgehammer to the fourth wall, some elements will remain uncertain until put in front of an audience – the "missing ingredient".

"I'm hoping, if I live to the first performance and don't die of exhaustion, that I'll suddenly realise the joy of theatre – that immediate response and feedback," Heap says. The show, which its breakneck visual gags and more costume changes than a Lady Gaga gig, is an unforgiving reintroduction to the stage. At the very least, Heap jokes, the punishing pace will keep him fit. "They will say Mark is doing his usual mad thing, but looking a lot thinner."

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