Almost 90,000 pupils risk being priced out of private schools, warns MTM Consulting, which advises both state and independent schools on business matters. Between the end of 2001 and 2006, fees rose by 39 per cent, compared an 18 per cent in average earnings.

The 14 per cent of private pupils from non-professional backgrounds almost 87,000 are particularly vulnerable to fee increases. At least 31,000 will leave the sector if fee increases are not curbed, says MTM.

Only a minority of over-subscribed schools will be able to charge higher fees. The smaller or less popular will have to cut costs.

“That means challenging such sacred cows as a pupil-teacher ratio of less than one to ten; offering a wide range of minority subjects; and commissioning prestige projects such as luxurious sports and theatre facilities,” says the MTM report.

Gavin Humphries, its author, said schools were beginning to find that affordability was affecting their ability to attract pupils.

Over the past 10 years, the proportion of children educated at independent schools has risen from 6 to 6.3 per cent. But since 2001-02 the number has “barely risen”.

Problems attracting enough pupils able to pay full fees led William Hulme’s Grammar School in Manchester to switch to the state sector this month.

Stephen Patriarca, its head, said it was the only way to secure the school’s future. At least 30 other independent schools could follow suit by becoming academies.

But state schools are not likely to become more attractive to independent school parents over the next five to 10 years, says the report.

Independent schools could form federations, saving money through economies of scale. This could also help them meet new “public benefit” tests, which assess whether they are open to the poor in order to retain their charitable status. This saves them around pound;100 million a year in taxes. But if rising fees narrow the social class of new pupils, the independent schools’ public benefit case will be weakened

The report comes a month before the Charity Commission begins a round of consultation on the tests.

Jonathan Shephard, chief executive of the Independent Schools Council, called the report “melodramatic”. “Affordability is recognised as an issue by ISC schools, which endeavour to keep their fees as low as possible,” he said.

“The fact remains: numbers have risen in 18 of the past 20 years. Costs are an important factor, but not the only driver in the choice of independent education.”