Lucy Hawking dips into her rucksack, pulling out a handful of space rocks (the sweet kind) which she kindly gives me for my children.
She's been doing a series of book events for children, she tells me, fishing out a miniature Simpsons doll of her father, Professor Stephen Hawking, complete with wheelchair (in honour, presumably, of his cameo in the show), and some freeze-dried ice-cream as eaten by astronauts, which she uses in her presentations.
It's fun stuff, the kind of eye-catching fare which would make youngsters sit up and listen to snippets of science.
And it's a clever introduction to her new children's book, George's Secret Key To The Universe, the first of a trilogy written in collaboration with her famous scientist father.
Single mother Lucy (36), who has a nine-year-old autistic son, William, is bright, witty and easy to talk to - unless you veer into her family's personal life.
She is fervently protective of her father, refusing to answer questions about his private life or about his ex-wife Elaine, who faced accusations of abuse three years ago amid stories that he had been cut, beaten and left out in the sun on the hottest day of 2003. Prof Hawking has always denied the allegations.
That period, coupled with the disintegration of Lucy's own marriage to William's father, Alex Mackenzie Smith, a former member of the UN Peace Corps in Bosnia, led her to a descent into alcohol, which resulted in her spending a month at a clinic in Arizona.
Today, sipping mineral water, she simply wants to move on, she says, and deal with the much happier place in which she finds herself with her father.
"Life is not a bed of roses for anybody. Everybody goes through desperate periods.
"Hopefully, with the support of family and friends you come out of it and you are allowed to move on.
"Where we are today, I live in Cambridge and we spend a lot of time together. My son and I went on holiday to Corsica with my dad this summer, which is the first time we've taken my dad on a real family holiday."
She won't elaborate on the years of her father's second marriage, in which she didn't see so much of him, but working on the book has, they both agree, brought them much closer.
The story centres on two children, George and Annie, who access the Solar System through a fantastic computer called Cosmos. Annie's father, Eric, is a brilliant scientist, but Lucy says he's not a mirror image of her father.
"Eric isn't my dad, but he has elements of my dad's personality - he's very affable, friendly and has a childlike sense of wonder and curiosity.
"He has a tremendous sense of kindness which I very much associate with my dad."
The story not only focuses on George's adventures but also features fantastic facts about the universe and the planets, including Prof Hawking's latest ideas about black holes.
"I'm the creative writer and obviously he's a very famous theoretical physicist. He has this great enthusiasm for explaining complicated subjects in simple terminology.
"We brought different skills to the project. I'm not about to start correcting his physics.
"We did have some disagreements. They were largely when I wanted to do something creatively which would involve bending the rules of physics."
Lucy can only ever remember her father, who has suffered from motor neurone disease since the age of 22, in a wheelchair, although she knows that when she was born he could still walk with a stick.
Today, she is totally used to the fact that the 65-year-old Cambridge University professor, whose book A Brief History of Time has sold more than 10 million copies, can only communicate through a tiny muscle in his cheek.
When he clenches it, a tiny detector attached to his spectacle frame passes on information to a computer, which enables him to form sentences.
However, there can be a long time delay while the computer deciphers what he wants to say via a speech synthesiser.
She laughs at the suggestion that at dinner parties the topic of conversation may have changed by the time his contribution is made.
"You realise how much you say is jabber," she smiles.
Lucy is one of three children from his first marriage to Jane, a language teacher.
Both became involved with other people - Stephen with Elaine and Jane with Jonathan Hellyer Jones, whom she went on to marry, before the Hawkings divorced in 1990.
Ironically, Lucy and her parents now all live near each other in Cambridge, so she sees quite a lot of them. And Jane is now included in the family get-togethers. It's all very civilised, she explains.
Growing up in a world of science, Lucy was always the actress, the frivolous one, she reflects.
She read French and Russian at Oxford University before becoming a journalist, and has had two previous novels published.
"There was science all around me. I was curious, but it wasn't where my interests lay. It was so clear that I wasn't going to be a scientist.
"My dad did suggest it to me because he genuinely believes that a career in science is the most exciting career that you can have, that you are on the cutting edge of something. But he accepted that it wasn't really me."
Was it difficult living with such a brilliant man?
"When you're a child you accept what is around you as your normality. It's only when you get older that you can look at the situation you are in and see the differences to other people's lives."
As her father's career flourished, so his body degenerated, says Lucy. "It became harder for him, particularly when he started to lose his power of speech. When you have a communication problem it is frustrating, especially when your mind works very fast.
"But he's very good at putting a positive spin on things. He's had to develop an economy of style. He writes in an evocative but concise manner, which is a great discipline."
Has his fame made it difficult for her to step out of his shadow?
"Anybody with a very famous relative is always going to be referred to in connection with that relative. But I'm very proud of him," she says, protectively.
Indeed, Lucy has had enough on her plate juggling a full-time writing career with looking after her autistic son.
She is currently planning George's next adventures and will be joining her father at the forthcoming Bath and Cheltenham Literary Festivals.
"We want to inspire children's curiosity and fire their imagination," she says.
With her creative sparkle and his scientific genius, children should be embarking on exciting imaginary trips across the Solar System for years to come.
George's Secret Key To The Universe, by Lucy and Stephen Hawking, Doubleday, £12.99.