Cross the threshold into Julia Donaldson's home and it feels as though the house is greeting you as much as its owner. It's friendly. Worn floorboards, high ceilings, doors ajar to rooms with big comfortable furniture. There are books, knick-knacks, lots of photographs pinned to boards. Donaldson leads the way to the kitchen that has an alluring entrance into a side room, all shelves, with bright props spilling out of boxes. Her husband Malcolm appears, offering coffee, and as Julia settles down at the table she says wistfully that the place is a little bare. "The house may look cluttered, but it's actually…" She looks around. "There was loads of…" She points to a row of cupboards, bare on top. "All the broken things, but which looked beautiful from a distance, were up there…"

Julia Donaldson doesn't speak in rhyme. Of course she doesn't. But it almost wouldn't be surprising if she did, given her status as towering giant in the world of children's books. Many of her 160 books, which span plays, picture stories, novels and educational books, are in rhyme, and her name has become inextricably linked to jaunty verse and easy rhythm. In real life, though, she manages to articulately conjure up a vision of what she's describing, while often not quite finishing sentences and half-saying words. It's as if her sentences leave a whimsical trail in the air, waiting for the listener to catch the thread and weave their own end.

Donaldson's success has been a little like that – she started the sentence, and everything else aligned to finish it in a rather different way than she intended. Until 1993, when her first picture book, A Squash and a Squeeze, was published, she was a freelance songwriter. She was 44 when a publisher approached her out of the blue, turning what had been a song into a book illustrated by Axel Scheffler. Which was fortuitous timing, because cost-cutting at the BBC, which she often wrote for, meant that work was drying up. She remembers quite clearly being "prostrate on the floor, banging my fists and yelling" in frustration around this time, as freelancing was becoming increasingly tricky.

Dynamic duo: Julia Donaldson and illustrator Axel Scheffler in 2007. Photograph: Murdo MacLeod for the Observer

That was her first encounter with Scheffler, the German illustrator based in London. It was going to be a long and fruitful relationship. For the next six years, aside from 17 educational books she penned, Julia Donaldson was a songwriter with just one book in the shops – until The Gruffalo, her story about a little mouse who imagines a monster (with terrible tusks and terrible claws and terrible teeth in his terrible jaws) that turns out to be real.

Who knew it would be such a sensation? Certainly not Julia Donaldson, nor Axel Scheffler (and not the other publisher she first sent it to, whose name she won't say, who sat on it for a year until she found a taker at Macmillan).

She couldn't have predicted that in 2014, 40p in every £1 spent on picture books in the UK would be spent on a Donaldson title. In 2013, and in the first quarter of 2014, she was the UK's number one bestselling author across all books – children's and adults'. Think about it: more than Harry Potter, more than Fifty Shades of Grey. On that kind of profit, some people start drawing up plans for underground swimming pools.

She acknowledges this while chopping tomatoes for lunch, a little embarrassed that they were able to buy a new house before having completed on the current one, but says she still lives frugally and loves bargains. Her trusty oven stands next to her, a silent and persuasive corroborator. It's one of those ones where the grill is head-height. It's not at all in the modern aesthetic, with its white plastic and small oven, but is practical and works fine. She isn't materialistic. The main difference money brings, she agrees, is the freedom – and she doesn't have to panic any more about Malcolm's boundless generosity, like she did when they were skint. He's a retired paediatrician, but when he's not teaching Malcolm is part of his wife's troupe (generally made up of anyone she can rope in to help), travelling the world, acting out her books. Earlier this year, had you been at the Bologna Children's Book Fair, you would have seen him play the fox from the Gruffalo – with a French accent – opposite a German owl (who happened to be Scheffler).

'Her husband Malcolm says: “She writes the words, I remember them.”' Pictured: Julia and Malcolm busking in Bristol. Photograph courtesy of Julia Donaldson

The songwriting career made sense – Julia grew up in a very musical household; her mother was secretary of the London Leader Group, her father put on concerts, and their house in Hampstead was always abuzz. Julia and her younger sister Mary lived with their parents, aunt and uncle, and grandparents – "Like Milly Molly Mandy," Malcolm says, walking through the kitchen – and the children were never short of someone to read them a story. It wasn't all idyllic, though; her father contracted polio when she was young, which left him using a wheelchair for the rest of his life. "I suppose children just accept whatever their lot is," she says. "It was all just fine. Then one time my mother… started to cry and suddenly… it came home to me that it was a big deal."

Her father had a cerebral job – he did a groundbreaking study on identical twins – so could continue to work, and still played his beloved cello, but those were the days when the world didn't cater for disability. "My father was a very lovely, gentle, patient sort of character naturally," Julia says, "but occasionally he would be frustrated and one day just flung the butter knife across the room. One time only he suddenly yelled: 'I wish I could walk.'"

She moves her head as she speaks, and her half-sentences flitting here and there are brush strokes, snippets of thought that paint a vivid picture. Her father died of a heart attack at the age of 59 – a big loss. It had been hard for her mother, who died just 11 years ago, but "they were tremendous companions," she says. The pair would discover old songs and her mother would research them. "One was called 'The Little Strawberry'. My mother spent hours in the British Museum – Malcolm used to laugh – trying to find who was the little strawberry. She never found out."

The house is emptier than usual because Julia and Malcolm are leaving. After 25 years in this old house just outside Glasgow, where they raised their three boys, Hamish, Jerry, and Alastair, they're moving to a small town in Sussex. There's the proviso of a flat in Edinburgh for regular visits to Jerry's children in Dundee. Alastair's children live in Oxfordshire, so they'll divide their grandparent time as equally as possible. It's a big job packing up – the removal men have been here once already – and there's a lot to go. "I've just taken over the whole house," she says, with a giggle. "You'll see."

It's always a poignant time, selling the family home, but these walls have perhaps witnessed more than their fair share of heartbreak amid the joy. Hamish, their eldest, killed himself in 2003. He was 25 years old and had lived with schizoaffective disorder, which had psychotic symptoms similar to schizophrenia and mood symptoms similar to bipolar disorder. She finds it hard to fix neat labels on Hamish's life. "The thing is, [the diagnosis] makes it sound like he was ill all the time," she says, searching for the words. "The main thing was just – well, I think he was sort of ill all the time – but in between crises he was a lovely, lovely boy, but he was just – somehow no one could handle, no one could cope with him right from the word go, the playgroup…"

Later she gives a tour of their photographs. Among the pictures of Julia and Malcolm in owl and pussycat costumes (from "a brilliant exhibition called 26 Characters in the Story Museum in Oxford"), their grandchildren, a boat, there's a photograph of a beautiful tousle-haired toddler, face upturned, giving his grandfather a kiss. The man is Malcolm's father; the little boy is Hamish.

The landline rings. "So loud because my hearing's…" Donaldson says, drifting into ellipses, as she leaves. It's her agent. A conversation ensues about the size of her name on a children's book she's written the foreword to: Donaldson felt her name had been too big on the initial proof, given she hadn't written it. They've just seen a version with smaller type – but should it be smaller still? She brings the book to the kitchen table to have another look. "They want to put my name on it because just at present that will help sell the book, but I don't want to seem swanky," she says, peering at it.

Monster success: the bestselling Gruffalo and The Scarecrow's Wedding, Donaldon and Scheffler's latest collaboration. Photograph: Macmillan Children's Books and Alison Green Books (an imprint of Scholastic)

What's funny is that while her name boosts other people's sales, the publishers often make sure that on her own books there's a "By the author of The Gruffalo" sign. By this rationale, the Gruffalo appears to be even more famous than Julia Donaldson MBE, Children's Laureate from 2011-13, who has her picture in the National Portrait Gallery.

This could be true. The Gruffalo has been translated into more than 40 languages (including Scots) and made into a touring stage play, an animated film (that had 9 million viewers when it aired on Christmas Day in 2012), and his toothy grin stares out from T-shirts, plates, mugs, notebooks, games, you name it. "I mean, I do feel quite like the mouse in the story," Donaldson says with her little laugh. "You know: 'Oh! That's the Gruffalo – I thought it was just in my imagination.'"

If you aren't embedded in the stage of constantly reading books to small children it might sound like exaggeration, but there is a real cult of Julia Donaldson. She doesn't deny it – can't – but tries hard to undercut the sentiment: "I think you get more appreciation than probably strictly you're due because parents so love their children that if you come in to that little magic world, they probably think you're more wonderful than you actually are."

It's not just the parents. Donaldson spends a day a week replying to letters and answering questions, many from children. A few of the funniest have made it to a pinboard in the downstairs loo ("Dear Julia I'm rubish at hand stabs bcuse I orwas forl over" or the one from an unfortunate teacher who wrote to Julia about "helping the class with there writing"). She fetches a pile of post and leafs through it, plucking out examples: "You get demanding ones just saying: 'Could you send me four books please'"; there's a letter from a mother thanking her for inspiring her dyslexic son – "so nice, isn't it"; someone in Russia doing a PhD based on her books; and – "this one made me laugh: 'Is your next book gonna have bad guys?'" She was able to reply a hearty "Yes!" given that her latest book, The Scarecrows' Wedding, out later this month, features a very bad guy. He comes in the form of Reginald Rake, a dandy (and scarecrow) who smokes cigars and nearly sets the goodie scarecrow, Betty O'Barley, on fire. Her granddaughter Poppy, who is four, absolutely loves it. "She loves accidents, you know," Julia says, explaining she's forever being asked to recount tales of her uncle Jerry getting burnt as a child, or how her dad Alastair accidentally poked a stick in Julia's eye.

Malcolm comes through the kitchen again. "You don't want to recite The Scarecrows' Wedding now?" he says. So in practice for next month's Edinburgh Festival, they stand together, arms outstretched like scarecrows, and tell the tale, including accents. And without props or exact words from Julia – Malcolm, modest about being word-perfect says: "She writes the words, I remember them" – it is still very edifying to be told a story. Edifying to meet the storyteller behind the story, too, and discover she is someone who keeps broken things because they look beautiful.

The Scarecrows' Wedding is out on 17 July, published by Alison Green Books (an imprint of Scholastic) at £12.99. To order a copy for £9.99, with free UK p&p, go to theguardian.com/bookshop or call 0330 333 6846 as of 17 July