In December 1988, my mother, then a junior health minister in Margaret Thatcher's Government, commented on television news that "Most of the egg production in Britain is infected with salmonella." Since the good people of Britain believed her, egg consumption fell by a third, the press went mad, writs started flying, colleagues disowned her and she eventually resigned.

The first I knew about this was when a sixth former at my boarding school approached me in the corridor saying, "Your mum's in the paper again." I had a quick peek at the copy of the Mirror he was brandishing and replied, "So what?" I already had a folder decorated with my favourite newspaper cartoons of mum's antics - she used to send the funny ones to us at school; I was blase about answering the phone to the Daily Mail. It wasn't until the holidays, when dad drove us to a strange flat in Kensington he had borrowed because the press were camped out at home, that I worked out that this was different. But I was only 11, so going into hiding was a big adventure.

That December, and in particular the way the press reported it, changed our lives. Mum never went back to being a minister, and soon after she started writing books. Although she was well known before then, and was tipped for a place in the Cabinet, she is now most famous for the "eggs incident" and the sex scenes in her parliamentary novels. I got a new nickname - "Egg" - and changed schools after it became clear that my old school did not know how to deal with press enquiries about their pupils.

A month ago, following Princess Diana's funeral, I was struck by one particular image. It was the photograph of Charles, William and Harry as the coffin passed them. Harry was in a world of his own. But both Charles and William were staring at the photographer, the look on William's face one of scarcely disguised hatred. A little over a week before, the boys had paraded in front of the cameras in an attempt to improve his image (not theirs). There was, then, too, the suggestion that William resented the imposition, but was doing his duty to help the family. As Andrew Morton retells their mother's secrets, William and Harry must know that their lives, as much as those of their parents, are public property. Do William and Harry ever want to be "just like the other kids"?

Famous parents have to make a choice. They can try to hide their offspring away, and do their best to have a normal family, or they can encourage the children to take an interest, maybe even get involved. Paul McCartney chose to hide his daughter, and now she has become independent of him and successful in her own right. Julian Lennon chose to follow his father into music, and his face is instantly recognisable.

The modern appetite for celebrity is insatiable. For politicians, royals, sports and media personalities, to name a few, fame is both a boon and a bore. Favourable press coverage, be it news, reviews, interviews or commentary, is one of the best ways of getting a message across, improving public opinion ratings, bagging a lucrative sponsorship contract, or, dare I say it, selling books.

Sometimes the children get involved of their own accord, posing for photos and volunteering for the regular "I am a famous daughter" interviews offered by magazines. At six I persuaded a television crew to film me pushing a wheelbarrow round our garden and asserted that Denis Thatcher was "Mrs Thatcher's wife, of course". I cringe now when I see photos of me aged 13 with mum in my messy bedroom, and a whole interview on how much of a smelly infant I was. There is also the exposure that goes with the parent's job (again, horrifying photos of Deb and I, but this time posed for the Conservative Party official photographer for an election address).

The flip side is that the famous become careful of what they get up to, wary and distrustful, and, with time, they may or may not learn what not to say or do. But every now and then someone slips up. It is all too easy to underestimate the impact of an off-the-cuff remark, not to cover your tracks carefully enough, or, perhaps, to trust the charms of a handsome Army major or a beautiful actress. When a scandal erupts and the feeding frenzy begins, the famous and their families hide and wait for it to die down. Or, as in the case of David Mellor, they persuade the wife and kids to pose for a family photo while they tell their side of the story. The spouse and sprogs are expected to stay supportively silent.

Fame can be glamorous, even for the kids. My friends are sick of me talking about my adventures on the QE2 last year, a luxury we could never have afforded had it not been for Cunard's need for celebrity guests on board. My sister has danced with Sting, and at an after-show party a few years ago Julian Clary sauntered past, pausing only to ask "Where have all the famous people gone?" First nights at the theatre, special invites to the parties afterwards, offers of "You really must come and visit us in Geneva!" - it is a tough life sometimes.

How are we, the children, supposed to react to our reflected glory or shame? A tough skin is an asset, as well as the ability not to believe everything you read in the papers or see on television. But in the end, there is the need to forge a separate identity, to become independent of your parents, both privately and as far as the public is concerned.

Did I want to be just like the other kids? Occasionally, perhaps, when the phone rang for the seventh time in an hour ("No, I'm sorry, the Curries aren't here at the moment... No, I'm the cleaning lady.") But I am lucky. I don't look like mum. I'm the boring, academic one. Anonymity is possible, if I so chose I could change my name or leave the country. But then, what have I got to be ashamed of? I'm not Edwina Currie's daughter for nothing, you know.