Until one of her daughters hired a genealogist to create a family tree for her 70th birthday, Kate Atkinson always believed her grandfather to have been among 45 miners killed at Bentley Colliery in Doncaster, following a devastating blast in 1931.

"I've seen the grave," she says. "It's very moving. All the men were buried next to their best friends. Every year, they still have a ceremony to mark the tragedy."

Then, two years ago came the surprising news that the man who died alongside his mates – after a sudden flash of ignited methane caused a catastrophic roof collapse, two decades before her own birth – apparently wasn't a blood relative at all.

"He married my father's mother and they had other children but he wasn't on the birth certificate," she continues. "I only have one photograph, the standard going-off-to-the-First-World-War shot, and he doesn't look like anyone in our line of the family. So maybe he wasn't my grandfather."

She pauses: "It's so strange, that urge to reach back into the past, it's to do with our own mortality I think; you want to feel those people, you want to know them."

Today, she has no idea who her father's father was. Moreover, at 36, Atkinson discovered she was herself illegitimate. Her mother had been unable to get divorced in time following a hasty wartime marriage, so her parents finally tied the knot when she was two.

"The mysterious first husband wanted to emigrate to Australia but he had to have his wife's permission, so they traded off and he gave her the divorce," she explains.

What was strangest, she says, was that everyone in her family knew the circumstances surrounding her birth – they just didn't tell her. As to whether any of it matters, she sighs: "The truth is that ordinary people are so much more complicated than people give them credit for. If I think of any of my friends, they've all got one of these backstories in their genealogy somewhere.

"I'm just really, really fascinated by the past, by history and the people who've been part of it because that's what history is, isn't it, the story of people?"

Which is a good point to introduce Atkinson's award-winning output, concerning, as it often does, extraordinary multi-generational stories of ordinary families navigating relationships of Gordian complexity, awash with glorious coincidence.

Her first novel, Behind The Scenes At The Museum, published in 1995 when she was 43, sensationally won the £20,000 Whitbread Book of the Year prize, beating such literary luminaries as Salman Rushdie, and went on to sell a million copies.

Featuring York-born Ruby Lennox as its central character, it followed six generations of women from the same family as it charted the social history of Britain. Like Ruby, Atkinson was a solitary, reading-obsessed only child growing up in York, where her parents ran a shop selling surgical supplies. That debut novel achieved something few writers do, marrying poignant reflection, laugh-out-loud wit and a cracking plot, subsequently an Atkinson trademark.

Indeed, having lived in Edinburgh for nearly two decades, she's quietly become one of our best-loved writers, garnering readers, sales and prizes by the bucketload.

Two decades ago, after a string of bestsellers, Atkinson, who began writing aged 30 after failing the oral examination for her PhD, almost certainly unfairly as a result of bitter inter-office politics at Dundee University, introduced her private eye Jackson Brodie – played in an acclaimed BBC series by Harry Potter star Jason Isaacs.

The genre-defying Case Histories was another sensation. A literary novel that just happened to be about crime. Stephen King branded it "not just the best novel I read this year, but the best mystery of the decade". Published today, the books would surely be labelled "cosy crime", which doesn't remotely do them justice.

Yet she remains slightly baffled to have written a crime series at all. Brodie – whose terrible childhood, multiple divorces and melancholic outlook would make him a PI from central casting were it not for his huge heart and unerring instinct for helping those in need – emerged almost by accident.

Atkinson admits: "I had these mysteries that needed solving and the person who solves them is a detective, but the minute you put a detective into a book, it's crime fiction.You just have to put that aside. It was really easy to write Case Histories and, with any book like that, I always think, 'I'll just carry on, the next one will be that easy, too' – which it wasn't.

"But I was still in that mode so I thought I'd do another one. I got to the fourth, Started Early, Took My Dog, and I thought, 'You've got to stop this, otherwise you'll become a genre writer'."

So she dipped out of the series and wrote a string of novels set during the Second World War, including Life After Life, A God In Ruins and Transcription.

Now five years after Brodie's last outing in 2019's Big Sky (her fifth and favourite of his books, so far), the ex-cop is back in a much-anticipated new adventure, Death At The Sign Of The Rook. Atkinson, it is clear, has lost none of her sparkle or wit. "He's marooned in a snowstorm in a country house hotel where a 'murder mystery' evening is taking place," she explains. "The real task was to get everyone into the hotel, so it's really the story of their journey towards that conclusion."

The country house in question, Burton Makepeace, and its world-weary chatelaine, Lady Milton, have been knocking around her brain for at least 20 years.

"They were always looking for a home. I wanted to write a murder mystery with Lady Milton in it. But I didn't want it to be the novel, I wanted it to be in the novel," she explains. "Then I thought it may as well be a Jackson Brodie book, it gives him something to do, so I wrote it in lockdown. I was just amusing myself, really."

With its baroque cast of characters, happenstance and wandering players, who pop up in the finale to perform the "murder mystery" event, it's an Agatha Christie-esque homage to Golden Age crime novels. It's also thought-provoking, contemporary and very funny. All of which makes Death At The Sign Of The Rook an absolute romp.

Brodie fans will welcome the reappearance of Reggie Chase, first seen as an awkward, intellectually brilliant 16-year-old orphan in 2008's When Will There Be Good News?, now a Detective Constable with a black belt and her own flat.

"She's a clever girl from a poor, sad background. She's got real grit and doesn't capitulate to Jackson."

Does the fact Reggie lost her parents reflect her creator's own complex family? "Not really," smiles Atkinson, a mother of two grown-up daughters, who has two grandchildren. "There's an orphan in all of us. I felt like an orphan, even when I wasn't one."

As ever, Brodie draws the eye. "Jackson's a sheepdog," she continues. "Because he's come from the head of a woman, he has a lot of female sensibility. It's hidden under a male cloak but a lot of the time he thinks like a woman.

"He's very chivalric. He's going to look after you. He'll punch the guy if necessary and, at the same time, he'll hold the door open for you!" Critics have sometimes given Atkinson a hard time for her frequent use of coincidence. Brodie often notes "a coincidence is just an explanation waiting to happen", but his creator is more forthright: "Without coincidence, that would be no fiction.Absolutely none. I love coincidences.

"A crime plot in particular really relies on them or you'd be struggling to get characters together. I'll never stop using coincidence, no matter what people say."

The late historical novelist Hilary Mantel once mused that Atkinson must have "a game plan more sophisticated than Dickens". So how does she come up with such brilliant stories? "I have a title, I have a beginning and I know where I want to be at the end, usually," she says. But she can't plan and it's the "in-between bit" that gets her into trouble, necessitating all sorts of frantic re-writing. "For a long time it's a rearrangement, not writing. It's a cut and paste," she admits.

Currently struggling with a book set during the 1951 Festival of Britain, she may decide to put aside for a few years, having become disillusioned with its writing.

While often described as intensely private, Atkinson is great company, well-informed, witty and fun. But the steely interior common to most great novelists, from Lee Child to fellow Edinburgh scribes Ian Rankin and JK Rowling, is there nonetheless.

We're talking shortly after investment firm Baillie Gifford has been forced by a small number of activists to withdraw from its generous sponsorship of book festivals over its (relatively small) fossil fuel investments. "I honestly don't know what the long-term prospect for book festivals will be without this kind of sponsorship," she says.

"I suspect that many other potential corporate sponsors will be put off in case they too are subject to 'purity' tests and show me someone who could pass one.

"We all know there's a climate crisis, people aren't stupid, but whether a small group of puritanical protesters shutting down arts festivals across the country is the way to go about ending it is open to debate - except, ironically, they're shutting down debate.

"I understand activism and the need to make your voice heard - I was arrested during the CND era of the Eighties – but there's an alarmingly naïve righteousness about the Baillie Gifford protest that does not draw sympathisers to their side and ultimately, I think, subverts the democratic process."

Her guilty pleasure, surprisingly, is Nothing To Declare, an Aussie documentary series that follows the country's Border Force. And she finds herself reading far less, especially while working on her own books, which is pretty much all of the time.

Which is sad to hear, I suggest. "It's not," she replies. "I've already read everything. I had a really good grounding in the classics because I did English at university and I was an only child so I started reading and carried on reading. I don't miss it."

That said, she regrets the fact modern children have so many distractions – and the libraries where she spent her childhood – appear out of favour. "I had an adult ticket at the age of six for York Central Library. It's a lovely building. Even now, I can smell the polish on the parquet. But today the shelves have sort of gone, the reference library is now genealogy."

Returning to Jackson Brodie, she'd love to see him back on TV – Big Sky was never adapted and Death At The Sign Of The Rook would make a perfect Christmas special – and believes Jason Isaacs would jump at the chance to play him again.

"We got on really well, they filmed in Edinburgh, and he's still the perfect age, so it's all there waiting." But she admits the complexities of TV rights make it tricky.

"I don't plan to kill him off," she adds with a flourish. “He must be well into his 60s now but he's not a codger. I've got several other books to write first if I'm spared, as the great Terry Wogan used to say, but never say never. Jackson's always looking for a plot."

Death At The Sign Of The Rook by Kate Atkinson (Transworld, £22) is out now. Visit expressbookshop.com or call Express Bookshop on 020 3176 3832. Free UK P&P on orders over £25