WHERE were you on August 31, 1997?

Denise Mina was living in Partick in a filthy student flat and had had the one and only massive argument she has ever had with the man she's now married to, the father of her two young sons. "He told me Diana had died and I thought, 'You know me so little. You think I'll be upset and make up with you.'

Why would anyone remember where they were on a given date years ago, the award-winning Glaswegian crime writer, graphic novelist, playwright and documentary filmmaker asked herself when plotting her latest book, The Red Road. Her 11th, and a cracking read, it is haunted by a historic crime.

Over coffee and Diet Coke, 46-year-old Mina – her pixie haircut rising like so many silvery stalagmites and subversive thoughts around her head – grins and says: "I can't even remember where I'm supposed to be now." She's referring to the fact that this interview is starting an hour late. (She forgot to check her updated schedule and was in the West End home she shares with her forensic psychologist husband, Steve, and their boys. She was in her pyjamas, playing on her computer, when she should have been in a Glasgow hotel bar helping me with my inquiries.)

She explains that she began thinking about the death of Diana, Princess of Wales – a generation's JFK moment – "because we don't just know where we were, we want to tell other people where we were.

"It's about narrative, strong narrative and the power of it, and what narrative can do," notes Mina, whose second Paddy Meehan book, The Dead Hour has been adapted for BBC1, with Jayd Johnson, David Hayman and David Morrissey. It will be screened early next month, following BBC Scotland's Bafta award-winning version of the first of the five books, The Field Of Blood. Meanwhile, her DI Alex Morrow novels are being conflated into a six-part Sopranos-style TV series by Hollywood director Ridley Scott's Scott Free company. All tell terrific stories, so they should make compelling television.

"People do love narrative," says Mina. "I think that's why writers have such high social status. After I first got published, people started treating me really, really well. People who had been quite unpleasant to me. I knew it was because they thought of me as a writer. Before I'd been this sulky waitress [at the Ubiquitous Chip].

"But the more I thought about it I realised it's because people love narrative. It's important to human beings. I think a lot about the power of narrative and what narrative can do, and how much we use it in our daily lives without even thinking about it."

Taking a surreptitious drag on an ersatz cigarette ("Stuck on them," she confesses), she adds that human beings have a fundamental need to believe that the world is fair, when it's plainly not. "Sometimes we have to create an afterlife where it's all fair in the end. It's not. We're fat Westerners. We're not better than anybody else. But narrative is how we make sense of death, for instance. We look for the narrative curve in someone's life."

Few crime novelists can create a more satisfying narrative arc – from a feminist perspective, too, thus subverting the genre. Her new novel begins with two brutal murders in Glasgow following the appalling sexual abuse of Rose Wilson, 14, on that fateful night in 1997. She is charged with the second killing when a morally ambiguous lawyer takes pity on her. Meanwhile, the brother of Pinkie Brown, the first victim, is charged with his murder.

Fast forward to today: Rose has served a short prison sentence and is rehabilitated, working as a nanny for the lawyer's family. Then, a man's body is found in the notorious, about-to-be-demolished Red Road flats. Fingerprints at the scene match those of Brown, currently on trial for arms dealing and in police custody. How so?

It's an impossible question, agrees Mina, explaining that, like her three previous Morrow books – which include The End Of The Wasp Season, which won the Theakstons Old Peculier Crime Novel of the Year Award – it begins with a question. "That's perfect detective fiction," she insists. "An impossible question is asked on the first page and on the last page it's answered, so there's this perfect parabola."

The question mark hanging over The Red Road is loosely based on the controversial case of former police officer Shirley McKie, accused of perjury after a fingerprint found at an Ayrshire murder scene in 1997 was wrongly identified as hers. (She was cleared and awarded £750,000 in compensation over the bungle.) "I was really interested in how the policewoman's fingerprint came to be where she could not have been – and the chain of events. Often the solutions to impossible questions are quite banal – somebody took the wrong bit of evidence to the wrong police station, say," Mina explains.

It's this immediacy that often makes her books feel as if the stories have been ripped from the headlines. Her last book, Gods And Beasts, just out in paperback, charted the downfall of a charismatic MP whose fictional fate recalled that of former Scottish Socialist Party leader Tommy Sheridan, while The Field Of Blood has echoe of the Jamie Bulger and Mary Bell child-killing cases. True crimes filtered through Mina's pitch-black imagination.

Her three, brilliant, "hardcore" Garnethill novels, with which she made her award-winning debut, are shot through with allusions to Macbeth. But she insists: "I hate people who write books that tell you what they've read. I don't f***ing care you've got an English degree. But you know what, I'm stealing off people all the time. We all steal off each other." Her heroine is Sara Paretsky, American godmother of feminist crime fiction. "It's always f***ing Chandler who inspired crime writers. Paretsky never gets her due. I LOVE her."

The Red Road also subtly references Graham Greene's Brighton Rock – the names Rose and Pinkie, for starters – although the sexual grooming of teenage girls by a gang of Asian men, in Rochdale, sparked the storyline. "I found that case very disturbing," sighs Mina. "It's always really vulnerable, chaotic, slightly unsympathetic kids who are trained up to be sex workers. It's been going on since time immemorial. We know this, yet they are treated appallingly by the police and disbelieved on the witness stand."

The constant in Mina's smart, salty, sparely written novels are her strong female protagonists, from Garnethill's hard-drinking social worker Maureen O'Donnell to would-be investigative reporter Meehan and tetchy Morrow, the permanently exhausted mother of twins. "For me, it's about untold stories, especially women's stories," says Mina.

The care and treatment of female offenders with mental issues was the focus of her PhD thesis, which she never completed because she wrote Garnethill instead. A former Strathclyde University lecturer in criminology and criminal law, she grew up across Europe as her father was an oil industry engineer. She went to boarding school in Perthshire and convent schools in London, Paris and Amsterdam, where she was "naughty and sullen". Back in Glasgow, she became involved in the women's movement.

When she wrote her first book, her publishers warned her not to mention the f-word in interviews. "Feminism!" she exclaims. "They said, 'You'll put everybody off.' Of course, people pretend that crime fiction doesn't have an agenda, that it's entertainment. But if you're dealing with the murders of, say, 20 prostitutes in Scandinavia that's regarded as incredibly political. Here, that's neutral."

Nordic noir is much on her mind because she's currently adapting the second of the Stieg Larsson Millennium trilogy as graphic novels. She has to take these overlong books apart, performing a forensic literary post-mortem. The Girl With The Dragon Tattoo is out now, in two volumes. "Larsson's own title, Men Who Hate Women, was so much better," she says.

Mina reckons that he knew the history of feminist crime fiction and thought, 'These are great books with a political message but they need more f***ing.' I have to say all the f***ing is completely implausible. I mean, everybody fancies this fat, bankrupt journalist. What is really interesting is that the corporate and the serial killer in the books are both psychopaths – and they're both conscienceless. I think those themes get lost since the books are quite flabby."

Why are we so hooked on noir?

"I think in the best crime fiction there's always a truth, a reality," Mina replies. "People like to read about serial killers because it's metaphorical fear. But I think that we should acknowledge that we're dealing with something dark and gratuitous. People read crime novels because they're a bit prurient. Maybe we should just 'fess up to the prurience and ask, 'Why do we want to be scared?' I believe it's because we're so safe.

"I certainly don't think people in Darfur are reading crime fiction, do you?" she asks before leaping on her Pashley Princess to cycle home to the graphic adventures of "the diminutive with the decoration".

The Red Road, by Denise Mina (Orion, £12.99). Gods And Beasts (Orion, £7.99). The Field Of Blood: The Dead Hour, BBC1, Thursday & Friday August 1 & 2, 9pm. Denise Mina is at the Edinburgh International Book Festival on August 13, 15 and 26.