"But then I realised he wasn't joking. He said no one ever wanted to do Kate's hair because it was so long and thick, and it was a bit of an issue.
"So I laughed and said I'd love to help out. It would be amazing to do Kate's hair, because it's so flawless.
"I was quite surprised, because to me her hair always looks perfect, like she doesn't have to make any effort at all. But it obviously must take time to make it look so good. I think any girl would still love to have Kate's hair though, even if it is a lot of work."
The Duchess's regular hairdresser is Amanda Cook Tucker, who was one of the first people to visit her in hospital when she gave birth to Prince George. She also travels with her on foreign visits.
During the Duke's visit to Centrepoint's health and well-being centre in Soho, central London, he also joined in a healthy breakfast session, where young people were learning about nutritional food.
But it appears that he might have been more interested in the treats on offer, given that Centrepoint tweeted that the Duke had a "sweet tooth" and included the hashtag #whoateallthechocolate.
The Duke, who later attended the Queen's pre-Christmas lunch at Buckingham Palace with his wife and other members of the Royal family, has taken a keen interest in the charity's work since taking up the post in 2005.
Seyi Obakin, Centrepoint's chief executive, said: "The Duke of Cambridge's visit provided a huge boost for all the young people he met ahead of Christmas, which for them can be a difficult and emotional time. We estimate that 15,000 young people will face homelessness alone this Christmas."
Hunting trophies including ivory and rhino horn may be removed from public display at the Queen's Sandringham estate following questions over whether they contravene European Union rules on endangered species. Royal Household staff are reviewing the 62 specimens in the trophy room at the Queen's Norfolk home, where the Royal family will spend Christmas.
The items, including a tiger skin and stuffed lions, could prove an embarrassment to the Duke of Cambridge, who has led a high-profile campaign to stamp out the illegal wildlife trade.