"It's about a lone boy who has this adventure on his own. For some strange reason, those were the kinds of stories that I enjoyed when I was a kid. Not that I had a particularly lonely childhood - I had loads of friends and a lovely family. But I liked books like Philippa Pearce's Tom's Midnight Garden and James and the Giant Peach and Danny, Champion of the World by Roald Dahl, which were all about lone figures. There's somehow something quite romantic about that."
Crook is a big fan of the late Charlie and the Chocolate Factory author, whose sardonic, subtly subversive work still captures young imaginations more than two decades after his death.
"[Dahl] brought just the right amount of irreverence into his books and a sense of humour that wasn't patronising," says Crook. "His characters are based in reality but they have a cartoonish quality and a grotesqueness about them. I love that dark side and kids need that to make it interesting."
While the idea for his story had germinated for 25 years ago, Crook only recently put his mind to completing it, spurred on by his two children, 9-year-old Jude and 4-year-old Scout.
"I guess I didn't feel confident that I had what it takes to write adult literature," he says. "My book is a very simple story. It's not vastly complicated and that's how I wanted it to be. I have a young son I read to and I wanted to write something he would enjoy."
As it taps into ancient British legends, The Windvale Sprites shares some spiritual ground with Jez Butterworth's tremendous play Jerusalem, in which Crook has played hapless wannabe DJ Ginger since it first premiered at London's Royal Court in 2009.
The most successful British play since Alan Bennett's The History Boys, the original cast completed its final West End run last month at the Apollo Theatre, just up the road from the private members' club in which Crook and I meet.
"The story of The Windvale Sprites has been with me for a lot longer than I've been doing Jerusalem but it showed me a direction I could go in," he says. "They're both celebrations of the mystical and the mythical."
After he had finished the text, Crook worked on the book's elegant illustrations when he was based in New York for six months last year during Jerusalem's sell-out Broadway season.
"That was always going to be a big part of it, because I've always drawn pictures," he says. "I wanted the opportunity to do something professionally instead of just doodling or drawing pictures for others."
Set in the fictional Cottingley Woods, Crook's book pays tribute to the young cousins Elsie Wright and Frances Griffiths, who astonishingly convinced many so-called experts - including Sherlock Holmes creator Arthur Conan Doyle - that they had actually photographed fairies in the countryside near their Bradford home.
"That's a reference for anyone who wishes to pick up on it," says Crook.
"I loved that story as a kid. It's astonishing that these girls could fool such eminent scholars and important people, because you look at those pictures now and it's pretty obvious they were cardboard cut-outs. But at the time, people didn't see that and it's strange that their eyes saw so differently from us. The idea of 'what if they had actually found a fairy?' was a big influence on the book and while they admitted they faked the photos, one of them still claimed they saw things in those woods."
Instead of charming Tinkerbell-style creatures, Crook's sprites are dragonfly-esque insectoids that definitely aren't human. "I was fascinated with the myth of the fairy and where it could have come from," he says. "It's like the myth of the mermaid, which, it's said, came from mannites or sea-cows, which were spotted by sailors and, through Chinese whispers and hazy memories, were turned into these beautiful, voluptuous women. I was thinking of what could be spotted fleetingly or from a distance that could be turned into this myth of a magical fairy with a wand. It's like the root of that myth."
Crook balances his writing with his more famous acting roles, including his recent turn as a smuggler in Steven Spielberg's The Adventures of Tintin. He had been planning to visit New Zealand for the role: "We were going to go to Wellington to do some ADR [automated dialogue replacement] work but then they realised that in this day and age you can do that via modern technology so you don't have to fly an actor halfway across the world for two days' work," he says.
"I did that film nearly three years ago now; it's taken a long time to finish it. But I had an incredible time, living in Santa Monica and working with Steven Spielberg."
The Windvale Sprites (Faber & Faber $28.99) is out now.