Westminster school, alma mater of Sir Peter Ustinov, and Winchester college, where there has been a caretaker head since Dr Nicholas Tate left a year ago, want the top jobs to be filled by summer 2005.

The posts have yet to be advertised. However, insiders say they are expected to offer salaries of at least pound;100,000 and generous perks which include a house, car and free food.

The two schools, along with Eton and William Hulme grammar in Manchester, are at the centre of an investigation into alleged fee-fixing.

And the appointments will come just a few months after the Office for Fair Trading is expected to report its findings.

Private-school insiders said they did not believe the inquiry would deter applicants but the independent sector is now understood to be finding it harder to recruit staff to top jobs.

Dr Martin Stephen, chairman of the Headmasters and Headmistresses Conference, said there were fewer applicants for private school headships now compared with 10 years ago.

“There is no doubt the field of applicants has narrowed,” he said. “But there is no crisis yet in the recruitment of private school heads although we are keeping an eye on developments.”

Dr Stephen is leaving the pound;6,441-a-term Manchester grammar this summer to become head of St Paul’s boys school in London, alma mater of the BBC’s John Simpson.

Manchester grammar has appointed Dr Christopher Ray from John Lyon school in Harrow, Middlesex.

Other private schools seeking heads include Tonbridge school in Kent, Hereford Cathedral school and Bryanston school in Blandford, Dorset.

The number of headship adverts in The TES for private and state schools is at its highest for seven years for the first quarter of a year.