Peaches: I earn £250,000 a year

In fact, Sir Bob's precocious daughter claims that she is already earning at least a quarter of a million pounds a year.

Peaches, who as well as writing regularly for newspapers and magazines has hosted two documentaries for Sky TV, makes her boast on her personal website.

She describes herself as a 'writer, journalist, documentary pro, mover and shaker'.

And she goes on to detail her income as '£250,000 and higher', although it is not clear how she arrives at this figure.

While she writes for the Arts section of the Sunday Telegraph, her employment as a columnist for the fashion magazine Elle-Girl recently ended when the publication shut down.

And last night a friend said: 'She was being a bit mouthy and joking around and I don't think she earns even a fraction of that.'

Peaches hopes to add to her fortune by finding success as a DJ along with her friend Fifi Brown. Together they call themselves the Trash Pussies.

But judging by their debut performance this week on Ibiza, a lot more practice is needed. Peaches took a break from a family holiday in Majorca to appear with Fifi at a music festival.

The pair spent 90 minutes doing little more than putting in CDs and pressing the play button, to the dismay of many ravers who booed and heckled them.

Peaches, who studies at the £15,000-ayear Queen's College in central London, later rejoined her family in Majorca.

Unlike her mother Paula Yates, whose life was claimed by drugs at the age of 40, she insists she steers clear of the excesses of celebrity life, saying: 'I don't do drugs. I don't drink. I don't smoke, I'm a good girl.'