The Recruitment and Employment Confederation said the figure was a conservative estimate of the number of supply days each week that agencies are unable to cover for teachers either sick or on training days.

Bob Wicks, chief executive of Select Education and chairman of the confederation’s education division, admitted that his own company was missing out on 2,400 potential bookings every week because of the shortages. Select, which finds supply teachers for 12,000 positions each week, could boost its business by 20 per cent if it could recruit more staff.

The confederation is now surveying all of its members and Mr Wicks said:

“Contrary to what the Government says, there is a very serious shortage of teachers.

“God only knows what would have happened if the country had had a serious bout of flu this year. Huge numbers of schools would have closed because of the difficulties of finding staff to fill the gaps.”

But new figures suggest that government initiatives may have contributed to the problem by increasing schools’ demand for staff.

The number of supply teachers working on contracts of one month or less has risen by a third, from 12,600 to 16,700 between 1996 and 2000, school standards minister Estelle Mrris revealed in a written parliamentary question.

Headteachers are now scouring the world for recruits, often interviewing and appointing by the telephone or via the Internet without having met the applicant.

One desperate comprehensive in the East Midlands, which has seven vacancies, is paying half of the air fare for a Canadian teacher to come to the UK.

Others have extended the global search from Australia, New Zealand and South Africa to Mauritius, Jamaica and Japan.

The head of a comprehensive in the South-east, looking to fill four vacancies, has arranged bed-and-breakfast for supply teachers and has even offered to accommodate a teacher herself.

“Supply staff have vanished,” said the head of a comprehensive in North Yorkshire and the Humber. “I have stopped looking for someone good. I’m looking for someone (fairly) warm and (fairly) vertical.”

Heads responding to the TESSHA survey were often critical of the calibre of supply staff, complaining of low expectations and poor classroom control. Where there was praise for supply staff, it was usually coupled with complaints about the cost and the high level of turnover which created instability for pupils.

But said John Fairhurst, head of Shenfield high, Brentwood, Essex: “Agency staff from Australia have been good quality - but the turnover is rapid and the sense of instability is not good for the children.”