Meeting illustrator Helen Cooper one morning in central Oxford opened my eyes to the complexities of children’s picture books. I had throught of them as charmingly simple things: short, easily graspable stories lit up by magical illustrations, used by parents to entertain or educate their offspring, or send them blissfully off to la-la-land.

But Helen shatters my assumptions. “I put in quite sophisticated things, almost to amuse myself,” she says. “And adults will read these books up to 20 times. I want them to keep on discovering new things.”

Her latest book, Dog Biscuit, aimed at young children, tells the tale of a wide-eyed little girl called Bridget, who ventures into a shed, where, overcome with curiosity, she eats a dog biscuit. She feels an itch behind her ear, starts sniffing the air and finds herself saying “woof”…well, you probably get the gist of it.

At less than 30 pages, this shaggy dog story — alive with wonderfully kinetic pictures of hurtling hounds and sausages raining from the sky — seems joyously uncomplicated. But look again: as Bridget morphs into pooch form, one building has a suggestively dog-like aspect. In a story starring a West Highland terrier, the architecture is in the style of Charles Rennie Mackintosh’s Hill House in Glasgow. Look even more carefully and you’ll see one stained glass window is also uncannily canine, if in an abstract way.

“Some people might see these things and some not,” she says, revealing more of her clever curlicues. “But the thing is that you’re never quite sure how your brain is working.”

She comes across as part-dreamy artist and part-pragmatist, speaking in rapt tones of the Sheldonian’s enigmatic head-and-shoulder busts, then launches into a business-like analysis of the current publishing market. I get the sense that she invests a lot of herself in her books. She never went to art college — ‘when I thought of going, I looked around and I felt that people were spending a lot of time trying to be different but they were being different in the same way,’ she says — and is completely self-taught. She spent years frequenting libraries, taking out book after book on drawing and illustration. “I studied and studied. I was quite obsessive for many years.”

She has a nice analogy for her job: that composing a children’s book is “not unlike film directing”. You write the text first, a bit like a screenplay, then create a world, as if you are a locations scout. Then you put a casting director’s hat on, trying out different characters for your parts, then finally you have to think like a camera person: “From which angle do the readers best need to see this scene? Am I coming in from the top? Am I coming in with a close-up? I always want to create an emotional intensity.”

She lives in Summertown with her American husband, Ted Dewan — also a writer and illustrator — and their 11-year-old daughter Pandora. They often visit the Pitt Rivers Museum or the Ashmolean, sketchbooks-in-hand, to spend hours doodling. The architecture of the city also often captures her thoughts, as does the history of Oxford. “It’s a very exciting place to live because of all the stories here. They’re strewn on the ground like leaves.”

Now 46, she grew up in Cumbria — ‘lots of sheep, a very remote place’ — where the lack of other children to play with stoked her fertile imagination.

She loved drawing and had a vivid inward world, although she also had the odd real adventure as well. Dog Biscuit is based on the time she sneaked into a shed with a naughty boy called Patrick; they ate a dog biscuit and were later told by Patrick’s straight-faced mum: “You’ll go bow-wow and turn into a dog.”

Although she was published at 23, she didn’t think that she could actually make a living out of it, and “for many years that was right, although eventually I did”.

Her advice to budding children’s authors? “Know that market and learn to draw. Practise and practise. We always say to children when we go into schools that something terrible is going to happen to you when you are ten. You are going to look at your pictures and say: ‘well, that’s not very good’. Most of you will stop drawing; that’s why most adults draw like ten-year-olds. But the people who don’t stop can normally draw quite well. That’s all it is. Repetition.”

l Dog Biscuit is published by Corgi, £5.99.