When she was four or five, Sophie Dahl was staying at Gipsy House, her grandfather’s bohemian home in Great Missenden, with her best friend Emily. The girls were sleeping in the guest bedroom in two little twin beds and her grandfather, Roald Dahl, came in before they went to sleep and told them the story of “a giant who blew dreams into children’s bedrooms with a trumpet”.

At the thought, Sophie’s enormous green eyes begin to glow with memory, her Mitford girl’s voice going rat-a-tat-tat before she pauses for a swig of lemon pressé.

“Anyway, we went off to sleep and then suddenly heard this scraping at the window. I remember it so vividly. I looked at Emily, Emily looked at me, and we both jumped into the one bed, clinging to each other and screaming. All we could see was this shape looming at the window, this tarrying man holding a trumpet and a suitcase,” she giggles.

“Of course I didn’t know at the time that both our mothers were down below holding up the ladder, mine shouting, ‘Please, dad, be careful! You’re going to fall down! You’re going to break your back!’

“We were too busy being ab-so-lute-ly terrified. It was only when we looked closer that we saw it was my grandfather doing the Big Friendly Giant, still wearing that woollen cardigan with the patches on the elbows.”

As Sophie relives high times in Buckinghamshire, where Dahl’s widow Liccy still lives today, it all sounds fantastic fun: japes in the garden, boxes of chocolates everywhere, rude poems recited at dinner. There were even a couple of tame ferrets.

And if that weren’t sufficient kiddie delight, the circus had an eccentric ring master. When The BFG — written for her — was published in 1982, Sophie, now 27, admits sheepishly, “I was the absolute envy of the playground.”

Later today, in front of 4,000 children at Buckingham Palace in the biggest event of summer (for which ticket requests exceeded 10m and caused the BBC website to crash twice), the erstwhile supermodel will take the stage as The BFG’s Sophie, the character named after her, in a play especially conceived for the Queen’s 80th birthday. The Queen’s Handbag is a 75-minute romp through the best of children’s literature; Lewis Carroll, Kenneth Grahame, AA Milne, JK Rowling and — at the centre of it all — Dahl.

Doubtless the old boy would have enjoyed seeing an ocean of children swarm the palace, eating 10,000 tubs of ice-cream and getting their sticky paws on everything. But more interesting is how, 16 years on from his death, Roald and granddaughter became the day’s main attraction. Has the time come for Dahl to reassert his precedence as our chief storyteller? After years of Potter-mania, is Rowling’s spell about to lift?

“Well, what’s interesting about the Potter phenomenon is that my grandfather’s books came before,” says Dahl. Are you saying she ripped him off, I ask, thrilled at the prospect of a stand-up fight between the two women at Sunday’s garden party?

“Well no,” she says carefully, “but JK Rowling has been very generous in acknowledging how she was influenced by him, and you can see it in Potter. My grandfather was probably funnier than her, and she is probably more epic, but it’s clear how like him she is in other ways. She’s interested in good and evil and, like him, isn’t at all afraid of the dark side of life.”

Taking a break from rehearsals at Buck House (“It’s so freaky going inside. I just pray I get to meet the Queen”), Sophie, now a resident of New York, arrives at the restaurant where we meet looking deliciously deb in Ralph Lauren polka dots. Time was I would have had to devote a paragraph or two to her weight, but I’ll just say that she is neither plump nor gaunt and leave it at that. None of that much matters any more. She couldn’t care less if she never modelled again.

“Oh, modelling could be as dull as anything!” she cries. “Then of course I flirted with the idea of being an actress, but I wasn’t a particularly good one.” If it’s no longer pictures, Sophie, then what is it? “Words,” she says.