When Julia Donaldson was first approached by Tron Theatre director Andy Arnold with a view to adapting her novel for teenagers, Running on the Cracks, it never crossed her mind that she should be the one to do it.

The Hampstead-born Bearsden resident is the current Children's Laureate, and has been responsible for the words of 184 books for children. One of these, The Gruffalo, became a publishing and story-telling sensation, has sold more than 10 million copies, been translated into 40 languages, is revered as a modern classic and been adapted for stage and screen. But the opportunity to adapt her own book was one Donaldson was happy to resist.

"If he'd said to do it, I could have," she says of Arnold. "I think I'm quite good at stripping things back. But the time comes when you have to step back and let them get on with it, and it's a different thing now to the book. The dialogue is very true to the book, but obviously there's a lot left out, and characters have been left out as well. I think it has become a lot more adult. After all, half the books written for adults are about children and adolescents, anyway, and that crucial time when they come of age."

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A hard-hitting tale of a runaway orphaned half-Chinese girl's flight to Glasgow in search of her grand-parents, Running on the Cracks deals with issues of mental illness in a serious and sensitive fashion, but writing an issue-based piece was far from Donaldson's intention.

"I set out to write a bit of a thriller about what would happen if this girl ran away to Glasgow and was taken in by somebody," she says.

"That turned out to be by somebody who was a bit crazy, which is where the mental health side of things came in. I didn't set out to put issues in. I just wanted to write a credible story, and they sort of crept in."

She may sound unsentimentally pragmatic about the play's content, but Donaldson has spent most of her adult life performing her songs and stories, both in theatrical and educational settings, and when she talks about her visits to the Glasgow theatre's rehearsal room she sounds positively star-struck.

"I had to pinch myself," the 64 year-old says. "Suddenly I was in the Tron talking with Andy Arnold about how he was adapting the script, and about set design. The shows I put on never have a set, and suddenly I had this flash-back to being a stage-struck teenager. That was really nice – and I'm not being blasé – but I don't really get excited any more if I see my name on a book."

One suspects it hasn't always been this way. Donaldson didn't have her first book published until 1993, after she'd been approached by Methuen publishing house two years before. The publishers asked if A Squash and A Squeeze, a song written by Donaldson in the mid-1970s for children's television show Play Board, could be made into a picture book, with illustrations by German artist, Axel Scheffler. Scheffler would go on to illustrate many of Donaldson's works, including The Gruffalo.

A Squash and A Squeeze opened the floodgates for Donaldson, who found a home for many other songs in illustrated book form. This gave her the confidence to write original works, including The Gruffalo and Running on the Cracks.

Donaldson started her career as a songwriter for children's television and radio programmes after a lively childhood of her own, during which time she understudied the fairies at the Old Vic theatre. While at university, she and some fellow students busked their way around France, and, with future husband Malcolm Donaldson, at rag week shows and functions. Once their education was complete, Donaldson worked in publishing in between co-devising touring shows around council estates in deprived areas.

In the 1970s Donaldson wrote songs for what can now be regarded as a golden age of children's television, which embraced creative learning on seminal shows such as Play Away and Play School. It is from this period A Squash and A Squeeze dates. Donaldson wrote musicals for children and ran workshops. While she dabbled with work for adults, it was always the child within that flourished.

"Some people shed skins and lose touch with everything they've done before," she says, "but I've never been like that. I've never lost touch with the various parts of my life."

The move to Glasgow more or less coincided with her move into the book world. "A Squash and A Squeeze was much more of a landmark book for me than The Gruffalo," she says. "It was very well timed."

As Children's Laureate since 2011, the same year she was awarded an MBE for services to literature, Donaldson has been active in protesting against library cuts, and this year publishes collections of 36 plays for early readers by various writers. This will be followed by another 24 for older primary schoolchildren, and a collection of poems to be performed.

"We've all been children," she says, "and given that so many people have an interest in children's books, they still only receive a very small amount of coverage and space in newspapers. It's only when something comes out about whether children are reading enough there's any coverage at all. So maybe children's literature is being taken seriously, but I'd still like to see it taken a lot more seriously."

Running on the Cracks, Tron Theatre, Glasgow, February 6-16. Visit www.tron.co.uk.