Jilly has set up a punishing itinerary of school visits “to open the eyes of this little private school girl” to the realities of education on both sides of the track.

“The basic idea is that the independent school in the book might lose its charitable status if they don’t really bond with the state school. They have to do a school play together and things like that. Of course, chaos breaks out. There is a really fierce rugger match. By the time the GCSEs come out, the rivalry is steaming,” she says .

While she is well versed in the private end of the market, Jilly admits she needs help on the state sector. She is typically effusive about the help she had from schools like the doomed Angel school in Islington and the “inspiring” Barnwood Park high in Gloucester, where a competition for a cover design for the new book brought some striking illustrations of pupils’ views of the gulf between state and private schools.

“They have been wonderful, incredibly trusting. I think some people are a bit nervous about being portrayed as sex maniacs or something but I am learning so much. The children are lovely.”

Jilly insists the new book, provisional title Magic Five after the five A*-C GCSEs so important in league tables, will be “her most serious yet”. But fans of her naughty bits should not worry.

“The hero is so sexy he makes Rupert Campbell-Black (star of Polo and Riders) look like a little boy lost,” says Jilly. “I’ve called him Feral Jackson. He is my first black hero. He is from the state school and is cool beyond belief. He cleans up completely among the boarding-school girls.” We promise to keep readers appraised of young Feral’s progress.