Kay is genial, agile and occasionally as bashful as a young boy. He often holds his forehead and grins in embarrassment as he looks over his work, and he describes almost every technique as having emerged from anxiety or failure. The happy accidents in A Monster Calls came about because he was too scared to draw (he thought the manuscript so wonderful it shouldn't be illustrated at all) and some of the ink splotches he'd made by printing with breadboards looked like hedgerows or trees.
As he shows me some of the work stored in his studio, he points out that most of his preparatory sketches for Harry Potter have gone. Not long ago, he says, he took a full carload to the rubbish dump.
Though Kay claims he hasn't yet arrived at a style - meaning that one day, when he stops trying to do new things all the time, work might get a little bit easier - there is a telltale love of creatures in his rendering of Harry Potter. Owls take centre stage and there are exceptional pages from a textbook on trolls and a guide to dragon eggs. The dog with three noses is rendered as if it were a much-loved and oft-drawn pet.
But it's true that he uses a wide range of techniques, from Ralph Steadman-like splats to Holbein-esque portraits to ghostly watercoloured landscapes, richly textured backgrounds and gnarly, impacted details that are all his own. Kay pulls out of a drawer an early sketch for his phenomenally finicky Diagon Alley panorama. Drawing it, he says, "was almost like knitting - you start at one end and move along". But others were much trickier. The Astronomy Tower was a building he could never get right - at first he thought perhaps a serpent could pierce the tower, but he still couldn't detach himself enough from reality.
Kay says that behind every final drawing, there are several attempts. And even when he's happy with the drawing, he adds colour and detail in separate sheets."It's partly because I had a terrible crash of confidence while I was doing it," he says. "Once I started drawing something, I was convinced I was going to ruin it, so I'd go on to a separate sheet, and another sheet, and another sheet ..."
Kay was born in a small town in Derbyshire in 1974. He is one of four children, whose father worked in insurance. As a child, he'd cover huge sheets of paper in detailed coral reefs: "I'd start in one corner really small. I realised the smaller I drew the more I could fit on the paper."
Although he studied illustration at university, and worked as an illustrator for a brief period (his first job was for the now defunct Soroptimist Weekly), Kay struggled to make a living. So he gave up, and drew nothing at all for 10 years.
Instead, he took jobs stocktaking carpets, packing calendars, filing medical records in a hospital. That led to a job in the archive at the Tate gallery, where he looked after the papers of British artists. One day, when talking to a friend, criticising some artist or other, his friend said: "Well, at least they're trying." He realised she was right.
Shortly after, the director of the Riverside Gallery in Richmond, who had seen his old work, offered Kay an exhibition. Though he hadn't picked up a pencil in years, Kay said yes. It was the most highly attended show in the gallery's history.
Thanks to his partner, Louise Clark, whom he met 13 years ago when she was a librarian at the Tate, he was able to make the leap back into illustration. The first year, he worked 360 days out of 365, yet when he filed his tax return he realised his profits from illustration came to less than £1 a day.
By the time he came to illustrate the books, he'd forgotten how he'd imagined the characters when he first read The Philosopher's Stone, years ago. The film actors had supplanted them in his mind, but once he went back to the books, he found he could make his own interpretation separate. He looked for real-life models wherever he could. Hagrid is, in part, an old biker who lives in Kettering, with the eyes of Winston Churchill. He was the first character Kay drew, and he set the viewpoint for the rest.
Mr Dursley is based on the local butcher. Hermione is based on Kay's niece. Harry was a boy he spotted swinging from the bars on the London Underground, and Kay had two stops to introduce himself to the boy's mother and persuade him to pose for him. "I'll be honest," he says, "it's the first time I've properly looked at people. I've never appreciated how varied we all are before."
Listening to Kay speak, you might think some uncertainty would be traceable in his work. It isn't. The result is fearless, exuberant and focused. But that won't prevent him from feeling anxious. "I can't tell you how worried I am," he says. "It's so public, Harry Potter." But then, he thinks, if it doesn't work this time, "we've got six more books to get it right".
Harry Potter and the Philosopher's Stone: the Illustrated Edition (Bloomsbury) is out now.