The Office for Fair Trading has been investigating claims for some months that four high-profile schools, believed to be Eton, Winchester, Westminster college and William Hulme’s grammar school in Manchester, regularly exchanged information on costs and likely fee increases in breach of the 1998 Competition Act.

A spokeswoman for the OFT said a significant number of schools had been served notices requesting disclosure of relevant information, which she said was not evidence of any infringement.

The Independent Schools Council appeared to acknowledge that some schools may have fallen foul of a change in the law - but sought to blame the Government for failing to keep them informed.

Jean Scott, Independent Schools Council chair, wrote to John Vickers, OFT director general, saying private schools had previously been exempt from the anti-cartel rules that applied to businesses.

“They are not a group of businessmen meeting behind closed doors to fix the price of their products to the disadvantage of the consumer,” she wrote.

“They are schools that have quite openly continued to follow a long-established practice because they were unaware that the law had changed.”

Mrs Scott wants the OFT to bring the inquiry to a close as schools’ legal fees mount up but fears it will not be finished before the end of the year.

After the launch of the inquiry last summer, the ISC issued a new code of practice on information, which had been agreed by the OFT, warning schools not to exchange commercially sensitive information.

Schools found guilty of price-fixing face fines of up to 10 per cent of three years’ turnover.

Private schools’ annual fees have risen by several times the rate of inflation in recent years and top boarding schools can charge pound;20,000 or more.