Scientists have found that girls as young as 13 are suffering from "Superwoman" syndrome – feelings of an overwhelming pressure to succeed – which can affect their mental and physical health. The results, published in the behavioural science journal Sex Roles, suggest that celebrities touted as an inspiration to young women may exacerbate their worries. Teenage girls feel inadequate when faced with the wealth of Paris Hilton, the literary success of JK Rowling, the sporting prowess of Dame Kelly Holmes or the iron dietary will of Victoria Beckham.

"What fuels disordered eating in some women is the desire to be the ultimate woman. Superwomen want the perfect life. No matter how well they are doing, they never feel quite good enough," explains Dr Janell Lynn Mensinger, who directed the study.

The personality traits associated with anorexia and other eating disorders – perfectionism, obsessiveness and approval-seeking – are also prevalent in high achievers and played out in the pursuit of success.

"The eating disorder is a coping mechanism to deal with the fulfilment of multiple demanding roles," explains Dr Mensinger.

According to the Royal College of Psychiatrists, anorexia is now the third most common chronic illness among adolescent girls, after obesity and asthma. Those between the ages of 13 and 19 are most at risk, with as many as one in every 150 15-year-old girls estimated to suffer from the disease, compared with one in 1,000 15-year-old boys.

The Sex Roles survey, in which almost 900 girls were questioned by academics in New York, suggests that socio-cultural factors have an impact on the development of eating disorders, with schools and peer groups especially formative. It was shown that those who attended "hot-house" schools, where there was more pressure to excel in both academic and extracurricular activities, were more likely to be afflicted.

Miranda Geddes-Barton, a 16-year-old pupil who attends Notre Dame College in Leeds, agreed: "There is so much pressure. It's definitely worse at a private school – A and B grades aren't good enough, and socially there are lots of cliques. Quite a few people have eating problems, and I'm sure photos of celebrities who are thin, pretty and successful don't help."