Leon is a famous daddy. Or he is to his daughter. He's on television as often as she wants him to be, reading and re-reading her favourite stories and waving goodbye to her at the end of each tale. In his DVD for the story Let's Go Home, Little Bear, Leon wears his regulation-issue grey sweatshirt. He reads to the camera. Sometimes the shot cuts away to a scene in the book or the characters from the pages appear, as if by magic, moving on the wall behind him. At the end of the tale, Leon asks his little girl to be good and to look after her mummy. After watching the story, Leon's partner writes to tell him how much his daughter — who wasn't even born when her daddy went away — adores the bedtime stories he sends her.

Leon is telling this bedtime story in a converted wing of Dartmoor prison. "He's never met his daughter — she just knows him as the 'man in the telly'," says Sharon Berry, creator of Storybook Dads.

We are watching the film at the prison. Suddenly, Leon stops in mid-sentence and his image freezes . "We need to go back and check the sound there and re-do the animation a bit," says Domonic, one of Leon's fellow inmates and unofficially the most valued editor on a scheme designed to allow prisoners to record bedtime stories for their children.

A survey by alltopbooks.com in June, revealed that one in three parents never reads bedtime stories, many claiming it's because they don't have time. In Dartmoor, where time is just what all the fathers do have, story-reading is a popular activity.

"On the outside, I read the odd story to my daughter," Domonic says. "But since I've been in here I've read her loads. She's five now and I've lost count of how many I've done.

"At first you feel a bit daft reading a baby's story out loud into a recorder. It's even worse listening to them being played back, the mistakes you make, how dull a story sounds. But her mum told me she loved hearing them and I worked hard to make them better."

The scheme was developed by Berry — an adult literacy teacher — using audio CDs. Then a visit by a TV producer inspired her to dabble in DVD stories and to introduce the puppets.

You would think going back on the wings known as the man who spends all day playing with kids' toys would be a bad move in prison, but it's quite the opposite. " Just by making a story in here, or writing your own ones like a lot of dads do, you're doing something positive ," says Domonic. Then he dons his headphones and sits at a PC under a barred window to digitally refine Leon's story. His co-editor, Chris, chips in: "It's because you're doing something worthwhile and you're learning new skills," he explains. "I worked in IT before I came in here so I'm good with the technical stuff. Domonic has learned loads. He developed the DVDs and the animation from scratch. He'd never really used a computer before he came here."

Terri Bailey, Berry's assistant and one of six "civilians" working on the project, admits they will miss Domonic when he's released. "He's great at getting the others to read comfortably. It's daunting when you first record a bedtime story, especially to camera, but he has a joke with them and it puts the nervous ones at ease," she says. "We keep joking that he should try to come back to Dartmoor!"

Dominic is adamant he won't be returning. "Doing the kids' stories is a reminder of what you're missing. I'd like to do a sound engineer or film editing job when I get out. I won't because of my record — but if ever they set up something like this outside I'd apply."

Storybook Dads already exists outside the prison system. Berry was asked to advise the army on setting up Storybook Soldiers after a chance meeting in 2004. Today, servicemen and women record bedtime stories and messages to their loved ones from Iraq and Afghanistan following the Dartmoor template.

On the day of our visit, an observer from the Royal Air Force Association is there too, taking notes on how the logistics of such a scheme might work for RAF personnel around the world.

"Back on the wings, it's all the typical macho, hard man stuff you probably expect prison to be," says Domonic. "But in the editing suite, you see a more human side. When they're talking about their kids or flicking through the storybooks or choosing which puppet they'll do a DVD with, you see some blokes soften up."

Bailey shows me files of responses from prisoners who have submitted stories. They contain lines about how their children have loved hearing daddy's voice and seeing him smile; some say the stories are better than the newspapers and magazines they get. There are cards on the sills at the barred windows from families thanking Berry and the team and photographs of Princess Anne watching Domonic in action at his editing desk alongside Terry Waite.

All the equipment and the civilian staff are paid for by the charity. Inmates don't pay to record stories on to audio CD, but there is a charge — equivalent to the cost of a week's tobacco — for those wanting to record a story on to DVD.

Not every Storybook Dad wants to record a DVD. Bailey plays us an audio story sent by an illiterate prisoner from another jail. He recorded Goldilocks and the Three Bears for his daughters, with the aid of a prison visitor. She reads each line and he copies her. Then the editors at Dartmoor edit out her prompts and add sound effects. On hearing the finished version, the prisoner said it was the best thing he had ever given his children.

But the editors left his final message untouched, with the imprisoned father's voice faltering and breaking up as he wishes his girls goodnight and sweet dreams and to tell them he'll see them again one day soon …

• Some names have been changed. For details see storybookdads.org.uk