There's no denying that, as a nation, we like our whodunnits.

What makes Russ Litten's new novel so appealing is that it turns the puzzle on its head and asks: "Who didn't do it?"

In Swear Down, an 18-year-old wannabe gangsta is found dead, stabbed in the chest, on a Hackney housing estate. Two suspects are in custody: 70-year-old Jack Shepherdson, a former merchant seaman, and black teenager Carlton McKenzie. Each swears that he alone was responsible for the killing and that the other had nothing to do with it. So which one is lying, and why?

The man tasked with making sense of their testimonies is Detective Sergeant Peter Ndekwe, newly arrived in his post and very conscious that his every move is being watched to see if he's up to the job. Ndekwe isn't the kind of copper one would normally find in a crime thriller. He's a strictly by-the-book, rules-following officer in a genre that depends on mavericks and loose cannons – exactly the wrong kind of policeman to invent if you were planning to write a series of sequels around him.

So it's just as well that writing a police procedural book was never Litten's intention in the first place. He says it didn't even occur to him that he was writing a crime novel until far into the process. The idea came to him through his work as a writer-in-residence in prisons, when an inmate told him about the legal term "joint enterprise".

"If two people admit to doing something," Litten explains, "the police have got to prove who didn't do it. It's not enough to prove who did do it, because if you can't prove the other person didn't do it the entire thing falls apart and both of them could walk free. So I thought, that's an original slant."

Litten, from Kingston Upon Hull, credits a story published in the Yorkshire Post when he was seven with setting him on the path to becoming a writer. In his teens, he was smitten by the books of the Beat writers, and later Charles Bukowski and Raymond Carver. For the past decade, he's made his living from writing of one sort or another, beginning with radio adverts, progressing to journalism and writing copy for those magazines that build up, instalment by instalment, into encyclopedias.

By 2008, he was living in Hackney, doing uncredited script work on the Guy Ritchie films Rocknrolla and Sherlock Holmes. He had an idea for a film that turned out to be too difficult to make, so he turned it into a short story instead. That led to his first book, 2011's acclaimed Scream If You Want To Go Faster, 10 interwoven tales set over the weekend of the Hull Fair.

By the time it was published, he'd moved back to Hull and secured a job as a prison writer-in-residence after the previous incumbent decided he couldn't cope with it. It's said that you meet the most interesting people behind bars, and Litten readily agrees. He's met a wide range of people inside, from young hoodies to white-collar criminals. Murderers, he says, can be particularly interesting, as it's often the only crime they've committed.

His is a role in which he feels he's made a genuine impact on people's lives. Even something as simple as helping a prisoner to write a bedtime story for his child can maintain the connection with family that might make a very big difference. "It did a lot of good," he says. "I know it worked. I had my - not misgivings, but I didn't know whether or not you could actually help people with creative writing in prison, but I've seen guys turn around through it."

As rewarding as it must be to help turn lives around, coaching incarcerated men to express themselves inevitably has its haunting, even harrowing, side."It tends to be the same story again and again," he says. "Absent fathers, abusive parents, drugs. We all know the scripts. But the aim is to try to transcend that, and try to get something positive from it. It can be tricky and it can be a bit wearing. With prison, the highs are really high and then you get the days when you think, 'Why the hell am I doing this?' But that's prison – everything's exaggerated."

Litten believes the experience has made him more compassionate – "We are all much better than the worst thing we've done," he says – but it's a job that required great sensitivity and discretion.

"You get a couple of weeks of training about how to conduct yourself and what to look out for, because you've got to be careful with creative writing. You can open up a lot of feelings. It's all right running a creative writing class outside and saying, 'Right, let's talk about your childhood Christmases.' All lovely, warm, nostalgic feelings. But with a lot of lads it could have been horrific. You've got to be a little bit careful.

"But at the same time it's an immensely liberating thing for lads locked up to get into creative writing. It teaches them empathy. It allows them to express themselves in ways other than violence and rage. So from that point of view it's a brilliant thing. The shame of it is that the Arts Council funding's been pulled for it all, so it's all coming to an end. The Writers In Prison network is having to be a charity."

Although not referenced directly in Swear Down, the English riots of 2011 seem to loom over it. The novel is set a year earlier, just after England's failed World Cup bid, and you can almost feel the tension building for a future eruption. Interestingly, Litten was given advance warning of one of the outbreaks from prisoners in his creative writing class.

"I remember when Hackney went up, and all the Manc kids were saying to me, 'Manchester's going to go up tonight', and I was like, 'Really? D'you reckon?' Because I had friends in Manchester, and it's a matter of pride that they don't just follow what London did. But once people see that there's not a lot of police on the streets, well -

"I think it's really, really strange, because you've got that many people who live their lives with absolutely no reference to the state. Lots of kids, they don't even sign on. They're invisible. So the agents of the state, ie the police, there's no fear any more of them. You see it at football matches. Whereas, in the 1980s, people used to run away from the police, now they run at them. So it's almost like people have lost not just respect for the police, but fear of the police. And that's because the state offers them nothing, so they don't acknowledge it. Which is a strange and terrifying place to be in, as a country."

Litten, who grew up on a housing estate – "but it was a happy place, not anything like the kind of estates we have all over the country now" – is cynical about the justice system in Britain, and about politicians who, he feels, treat it as a political football, shying away from drawing up long-term policies "in case they get voted out and the next lot reap the benefits". That's the kind of attitude that might fuel a crime writer's next novel but, as he's said, writing a crime novel was something he fell into by accident and he has no plans for another. In fact, Litten's next project is a ghost story. But not a typical one. As in Swear Down, he plans to turn the formula on its head.

Swear Down by Russ Litten is published by Serpent's Tail at £12.99