In a sign that the jobs squeeze is now hitting the nation’s top-performing schools, Thomas Telford in Shropshire has six vacancies.

Kevin Satchwell, head of the school - where every GCSE pupil last year got at least six good grades - expects difficulties filling a maths post.

He said: “Ten years ago when I advertised a maths post I had at least 100 applicants, this year I’ll be lucky to get 10.”

As well as maths, Mr Satchwell is looking to fill vacancies in art, geography, history, maths, business studies and English. “I think many people are under-estimating the teacher shortages,” he said.

“Schools are being forced to employ people who don’t have enough experience and then high salaries lock them into posts which they struggle with.” He added: “We need to make it simpler to recruit and train teachers.”

Staff at Thomas Telford teach four days a week and spend the fifth preparing for lesons.

At The Coopers’ Company and Coborn school in Upminister,where 96 per cent of pupils gained five or more A*-C GCSEs, headteacher Davina Lloyd advertised three times for a physics teacher with no response.

The 1,244-pupil school in Essex now has two vacancies: a maternity-cover post for two terms in history and a part-time vacancy in humanities.

Dr Lloyd said: “In all my 25 years in the profession I haven’t known it as bad as this. I just don’t think that anybody is out there at the moment of any calibre. We are an excellent school in a good area so I hate to think what problems other schools are having.”

Another high-profile school, Phoenix in the London borough of Hammersmith and Fulham, last week advertised 11 vacancies.

Head William Atkinson said recruitment problems were the worst he had seen in 30 years in the profession. “The standard of applicants has plummeted. I am sure some schools are appointing people that they would never have dreamed of appointing previously.”