If there lurks anywhere in an Agatha Christie novel a small boy, perhaps one who enjoys tennis or cricket and loves spending his school holidays at his granny's large house on the Devon coast, then that boy is almost certainly Mathew Prichard, the only child of the only child of the prolific author known as the queen of crime. Oddly, Mathew says he has never been asked before whether he has a cameo role in any of his grandmother's 80 books, but he rather thinks not. "It's not the kind of thing she would have done," he says. "My grandmother was fiercely private, especially when it came to her family."

But despite, or perhaps because of, her famed reclusiveness, the writer's private life has been the subject of endless fascination since her death in 1976. Now Mathew, 68, has provided a rich new seam of material with a book that describes a previously uncharted chapter of her life – a round-the-world trip she made in 1922. The book is in Christie's own words: it's based on letters she wrote to her mother, Clara, as she traversed the globe with her husband, Archie, for 10 months, having left their two-year-old daughter, Rosalind – Mathew's mother – at home in England.

The letters, Mathew explains, lay undisturbed in boxes at Greenway, Agatha's house in Devon, for many years until his mother died in 2004; but he always knew he would use the material for a book. The letters provide almost the only clues to one of the most baffling episodes in Agatha's own life – her doomed marriage to Archie Christie, who left her for another woman within a few years of their return to England. Mathew had a fascinating reason for wanting to know more about that because he never met his grandfather, although Archie didn't die until the 60s. When Mathew was a baby, his father – Rosalind's husband – was killed in the Normandy landings, so a relationship with his maternal grandfather could have been important to both of them. Why didn't it happen?

"I don't think my grandmother would allow it," says Mathew. "She wasn't even keen on Rosalind seeing Archie, though she could hardly prevent that – he was her father, after all. But she really didn't want me to be close to him."

Are we talking revenge? Could it be that Agatha – who built an incredibly successful career on the study of how determined and devious people can be when it comes to getting their own back – found a way of wounding Archie, decades after she was abandoned so cruelly? Her much investigated "disappearance" for 11 days in 1926, after Archie told her he was leaving, roused speculation that she was trying to make it look as if he had killed her. "I don't much like the word revenge," says Mathew. "But yes, I think she was possibly getting her own back. Archie had hurt her, and I don't think she ever forgot that. And it's certainly very unusual for a child never to meet his grandfather."

What emerges from the book is how very different Agatha and Archie were. His letters are short, fairly formal and to the point: her letters are long, effusive, and full of colourful descriptions of where they were and what they were doing – surfing was one enthusiasm and she was one of the first Britons to surf standing up.

They went to South Africa, Australasia, Honolulu and Canada, and Agatha basked in a new-found love of travel. The letters also show her starting to hone her skill of building characters: the Christies made their trip as members of a trade mission to promote the British Empire Exhibition, held in London in 1925 – the leader of the expedition, a Major Belcher, turned out to be, in Agatha's words to her mother, "a most unpleasant man" with an odious temper and delusions of grandeur who managed to upset the local dignitaries at every port. "You can't imagine how farcical it all is!" writes Agatha. "But at the same time very wearing, and spoils what would otherwise be such a pleasant trip."

The intriguing postscript to the tale, says Mathew, is that his grandmother again got her own back. "Belcher appears as Sir Eustace Pedlar in the 1924 book The Man in the Brown Suit," he says. "I don't want to spoil the plot for you, but I think if you read it you'd agree that he gets his comeuppance."

Mathew has fond memories of his grandmother who, he says, was "the best listener I've ever known". Because his father died so young, he and his mother were extremely close to Agatha. "We spent a lot of time with my grandmother, who I always called Nima," he says. "We'd have long, lovely summers at Greenway with her and Max, her second husband. She was always very encouraging and very generous. She was a voracious reader, and a great lover of theatre and the opera, and she really encouraged me to be interested in them too – I feel I inherited a great love of music and opera from her."

Agatha, he says, would never have said she was a great literary talent. "She never claimed to be a great writer. But the one thing she thought she could do was create an atmosphere through dialogue. And I don't think it would be too far-fetched to say that her letters to her mother as she travelled round the world helped her develop those skills – skills that would later be the backbone of her books," he says.

It is also clear that Agatha was realising the creative potential of throwing a group of disparate characters together, putting them in an exotic location, and then imagining the result if murder was to happen.

One of the most surprising elements of the new book is that Agatha left her daughter behind for so long. Mathew thinks his grandmother agonised over that. "She had this chance of a huge adventure, and she wasn't to know whether it would ever come her way again. But I think she really worried about leaving Rosalind behind – after all, in those days there was no modern communication, only letters which were both sent and arrived by ship."

But grasping the opportunity, says Mathew, was entirely in Agatha's character. "If I had to sum her up in a few words, 'enthusiasm' would definitely be one of them," he says. "She was hugely enthusiastic about life and what it held."

Why does he think she hit on murder mysteries as a genre? "She'd been a nurse during the first world war, and I think it had something to do with having learned a fair amount about poisons," he says.

"Also, she did toy with other genres – she wrote romantic novels under another name, Mary Westmacott. But the murder stories were more successful: she found she could do it, she got good reviews. So she continued with them."

That, in turn, assured her only grandson a lifelong career as chairman of the company that deals with her affairs, which are now a multi-million pound business. "After Oxford I worked for Penguin, the publisher, for a while, then Agatha's health started to deteriorate, and we thought it would be good for one of the family to run the business side."

Mathew has always felt lucky to be able to devote his life to his grandmother's work, and he doesn't resent the fact that people always associate him with her. "You occasionally hear someone say 'that's Agatha Christie's grandson'," he says. "And the one thing you can guarantee no one ever says next is, 'Who's she?'"

It is, Mathew agrees, a delightful irony that a woman who never gave interviews, and who didn't go on a single book-signing tour, became the most-read author in the world, barring Shakespeare and the scribes of the Old and New Testaments.

The Christie dynasty looks likely to run and run: Agatha is as popular as she has ever been, and Mathew's son James is being groomed to take his place. It was her characters who secured Christie's place in history: the Belgian detective Hercule Poirot, and the shrewd, understated Miss Marple, who – though she's generally thought to borrow many of her characteristics from Agatha's own grandmother – is also, Mathew thinks, based on the mother to whom she wrote from her round-the-world tour. "I think that willingness to believe that evil is possible in almost anyone, that in the wrong circumstances we can all commit terrible acts, was a family trait," he says.

Perhaps Mathew's most poignant discovery was that the Agatha who went round the world in 1922 was a different woman to the grandmother he knew. "She was much noisier and she had much more confidence in those days," he says. "On one of the ships, for example, she sang in public. And she had the courage to make that big decision to go away and leave her daughter for 10 months."

It's hard to get away from the thought that Archie's departure changed Agatha, and she never quite regained her early gumption after the divorce. Then again, according to Mathew, it was when she was up against it that his grandmother's writing became her lifeline. "At times of great family sorrow, what she held on to was her ability to write," he says. So perhaps if her private life, that life she guarded so jealously, had been less tumultuous, the world's bookshelves would not have groaned with quite so many Agatha Christie whodunits. And perhaps if she had not experienced Archie's devastating betrayal, she would not have imagined such devastating betrayals in the lives of her characters.

• The Grand Tour, by Agatha Christie, edited by Mathew Prichard, is published by HarperCollins, £25. To order a copy for £20, including free UK p&p, go to theguardian.com/bookshop or call 0330 333 6846