If there’s one question every child learns to loathe, it’s “What do you want to be when you grow up?”, usually because the adult who asks is all too ready to dish out criticism and throw in some unwanted advice of their own. But any adult still expecting to get the traditional replies of policeman, astronaut, teacher, doctor or racing driver, is in for a shock. Anyone quizzing a child today is more likely to hear, “I want to be famous!” Being Famous now counts as a career ambition all on its own. As children grow up in a celebrity culture, on first name terms with those who only use one name — Kylie, Posh, Jordan, Madonna, Beckham, Beyoncé — their own aspiration to celebrity increases.

“My daughter and all her friends want to be famous,” says Melanie Clough, mother of three children aged 16, 13 and 11. “They don’t say how. To be famous in itself represents success to them. It’s alarmingly shallow. When I asked my 13-year-old what she wanted for her 18th birthday she said a nose job and liposuction.”

When I was a child, most people wanted to be a vet. Those who didn’t might aspire to teacher or archeologist, all jobs which involved the dull business of choosing the right A-levels and training for years. Now, the ideal career is the instant one.

“The days when children wanted to be astronauts or fighter pilots is long gone,” the head teacher of a Surrey prep school told me.

“Perhaps 10 years ago I would have boffin kids who wanted to be a nuclear scientist, but not any more. Nowadays they want something far more nebulous, which is celebrity.”

Sebastian Scott, a former television presenter, now managing director of Princess Productions, which makes reality television shows, says he gets “hundreds” of applications from young people and the numbers are growing all the time. “The vast majority say they want to be researchers,” he says. “However, they really want to go straight on screen.

“They see celebrity as a quick fix for any problems in their life. They’ll be popular and rich. Being a celebrity looks like an unskilled job but the truth is that to be good is very skilled and takes many years. If people are propelled to fame before they have the skills to support it they become unstuck.”

Is this longing for fame a response to a culture that has demeaned traditional professions? Who would want to be a policeman when they’ve seen The Bill? Who would want to be a politician when they’ve seen the news? More youngsters voted in Pop Idol than the last election. Does it matter? When my four-year-old informs me she wants to be a pop star like Joss Stone, should I mind? It’s not as if anyone aged four wants to be a quantity surveyor or a financial services manager. And what’s wrong with wanting to excel? “Being interested in celebrities and aspiring to fame is not all negative,” says John Maltby, lecturer in psychology at Leicester University and co-author of a study on young people’s attitudes to celebrity. “Celebrity worship now provides an important reference point for growing up. It’s part of the transfer of attachment from parents to peer group. Also, whereas in past times family, friends and teachers were influential role models, celebrities now fulfil that role. The fact is that celebrity is so much part of our culture — on TV, the internet, magazines — and we need to look deeper at how its values influence our children.”

For parents of the wannabe famous, though, it’s the emptiness of the celebrity aspiration that concerns them. From lottery winners and reality TV participants such as Jade Goody, to tabloid kiss-and-tell characters such as Rebecca Loos, David Beckham’s friend, children are surrounded by images of those who have achieved fame through very little effort of their own. The media’s keenness to highlight the ordinariness of celebrities — their bad hair days, their spots, their grocery shopping — only increases the idea of the accessibility of fame itself.

And many would share the view of Katie, 9, who told me: “Being a celebrity isn’t boring, there’s always something to do and people wanting to meet you.”

Yet there are signs that children even as they crave fame, are aware of the downsides. They understand that their idols can crash and burn, or, like David Beckham, take knocks. They know fame comes in different degrees. “The kids who come to us understand there’s a temporary form of fame, which only a few people will make a lasting thing of,” says Scott. “Most of them know you’re famous for 15 minutes.”

Not, however, that he thinks it will diminish the desire for fame. “Celebrities are everywhere and they’re used to sell everything. When Liz Hurley and Sienna Miller feature in the newspapers instead of figures such as the Duke of Edinburgh, it’s no wonder that children want to compete in Big Brother rather than the Duke of Edinburgh award scheme.”