Fees increased by an average of 5.8 per cent this year to pound;9,777, though in Wales costs grew by 6.9 per cent - the biggest hike anywhere in the UK. Eighty-eight schools now charge more than pound;20,000, compared to none four years ago.

Pupil numbers dropped 0.6 per cent to 504,141 this year, the first decline since 1994, even though half of parents said they would be prepared to privately educate their child if they could afford it in a MORI poll commissioned last autumn by the Independent Schools Council (ISC).

The number of pupils in boarding schools, which accounts for almost all the most expensive places, has dropped by 1.2 per cent overall. The figures have been collated by ISC, which represents 80 per cent of privately-educated pupils.

They come as profit-making companies such as Global Educational Management Systems say they are poised to tap into the sector by offering parents a no-frills education at a fraction of the cost.

It wants 200 schools, with fees as low as pound;2,000-a-year, within 10 years, although critics are sceptical they could survive on such limited budgets.

But the ISC says that private schools have retained their market share nationally, as the overall school population dropped by 1.2 per cent this year. It blamed other factors for the fall, including a Government decision to double visa charges for non-EU pupils to pound;500, leading to a 10 per cent decline in children from overseas.

Jonathan Shepherd, the ISC general secretary, said the British Council was more obsessed with “filling its coffers” than promoting the British education system overseas. Numbers had also been hit by Labour scrapping the assisted places scheme in 1997, which put an end to government-sponsored pupils in private schools.