Two years ago, a novelist called Owen King had “the littlest germ” of an idea for a book: “What if, one day, all the women in the world don’t wake up?” He loved it, but it wasn’t the kind of thing he usually wrote. His novels, while well-reviewed, never exactly set the charts alight. Fortunately, his father – one Stephen King – was something of an expert in post-apocalyptic horror. “I thought to myself, ‘Wow, it would be just fucking horrible.’ I can tell my dad, it sounds like something he’d be really interested in.”

Discussing story ideas with his father wasn’t something he’d done before. “My dad is always getting pitched stupid ideas,” says Owen, sitting in his publisher’s London office. “If he goes to the corner store, there’ll be somebody who walks up and says, ‘Boy, have I got a horror story for you, Steve. I’ve got your next horror novel right here.’ But he loved it. And I was like, ‘Do it!’” Stephen initially declined this offer, but Owen did not feel capable of writing the story himself. So they did it together.

Emblazoned with both King names, Sleeping Beauties is the result. The Aurora virus is sending women around the world to sleep. If they wake up, they become violent. As men try to deal with a world without women – and those few women still awake try to resist the virus – the Kings focus on the small town of Dooling, West Virginia, where the inmates of a women’s prison, including the mysteriously powerful Evie, are dozing off.

Despite his dad being onboard, Owen had misgivings. “I was wary of someone reading the book and being able to say, ‘Owen wrote this and Steve wrote that.’ We have somewhat different styles – and I didn’t think that was going to reflect well on me. His books have sold millions and I didn’t want people to say, ‘This part is great because Stephen wrote it and this part isn’t so great because Owen wrote it.’ I just didn’t think I would get a fair look, you know?”

So they hatched a plan. One of them would write 25 pages, leaving gaps for certain scenes, then the other could rewrite those pages and fill in the missing scenes. And so on. “There are places where I could tell who wrote what,” says Owen. “But very few.” He calls it “a fantasy novel more than a horror. It’s pretty murderous in places – a lot of people getting torn apart and shot and dying gruesomely – but it doesn’t have ghosts, there are no scary clowns.”

Stephen King at his home in Maine, USA. Photograph: Steve Schofield for the Guardian

Owen has always written stories. His mother, Tabitha, is also an author, and he started delving into his father’s work as early as nine. “My parents had a policy: if you can read something, go ahead.” But he wasn’t sure it was the career for him. “My parents would retreat to their offices every morning and proceed to type for seven hours. You could hear it thundering through the doors. I knew they were in there alone and it sounded like the worst possible profession. I wasn’t sure I wanted that to be my life.”

Owen’s wife, Kelly Braffet, is also an author. “She grew up in a little town outside Pittsburgh. People would tell her, ‘Well, you can’t do that when you grow up.’ That wasn’t the way it was for me. You obviously could.”

As he grew older, he became more convinced of the path he wanted to take. He studied creative writing, going on to teach it to adults. He wrote We’re All in This Together, a collection of stories, and Double Feature, a novel. “They were literary books. They didn’t sell enormous numbers. I was very happy with what they did.”

Owen’s older brother Joe is another writer. He chose to submit and publish his work (Heart-Shaped Box, Horns, NOS 4R2, The Fireman) under the name Joe Hill. He was eventually outed as the son of Stephen when he started to appear at literary events and fantasy fans began to say: “Doesn’t he look familiar?”

Owen decided against a pseudonym, and was overwhelmed by the interest that ensued. “I thought people would take one look and say, ‘He’s interested in family comedy and it’s totally different.’ I felt I would be a bit more under the radar. I was naive. I did get a lot of attention. I rolled with it as well as I could.”

He’s sanguine about it today. “The biggest thing was that I never want anybody to be disappointed, to pick up something I wrote and say, ‘I was really hoping there would be a ghost in here and it’s just people being foolish.’ I recognise that the first line of my obituary will be, ‘Son of Stephen King’, and I’m comfortable with that. I think Joe’s gotten more comfortable with accepting that, too.”

As for Stephen, earlier this month he tweeted: “I and both of my sons are together on the NY Times bestseller list, Sleeping Beauties at #4 and Joe’s Strange Weather at #9. Awesome!”

Owen and Stephen have no plans to collaborate again, though the right idea might change all that. “I’m 40,” says Owen. “I have my own family, I live in a different place – it was just very special that we got to have basically this 10-month phone call. I got to spend this time with my father, and that’s not something you get to do as an adult. I treasure that.”