And perhaps more significantly heads regard as unsatisfactory 16.6 per cent or an estimated 4,246 of the teacher appointments they have made.

The head of a Dorset comprehensive said: “Fields for posts are very small.

Only one candidate has been suitable for each of the three teaching appointments we have this year.”

However, the picture is better than last year when there were 3,700 unfilled posts nationally and 19 per cent of appointments were considered unsatisfactory.

John Dunford, general secretary of the Secondary Heads Association, said:

“Teacher recruitment is not out of the woods yet, but there are encouraging signs that the situation is not as desperate in some parts of the country as it has been in recent years. The quality of many of those recruited is as high as it has ever been.”

The survey suggests that London schools have the biggest recruitment problems with an estimated 418 unfilled vacancies. West Midlands heads made the highest proportion of unsatisfactory appointments (24 per cent).

South-east schools came next on both measures with 329 and 18.7 per cent respectively. West Midlands schools have the third highest number of unfilled posts at 306 followed by East England at 228, the North-west with 149 and the North-east with 142.

The South-east has the lowest number with an estimated 60, with the East Midlands on 108 and Yorkshire and Humberside on 141.

Headteachers who managed to recruit high-calibre staff, such as Daphne West from the private Maynard school in Exeter, described themselves as “lucky”.

She said she had benefited from the move of the Met Office to the Devon city - providing a ready supply of spouses of relocating employees - and the general popularity of the South-west region.

But other schools have not been so lucky. One in the London borough of Harrow starts the new academic year with 13 temporary staff out of 65 - its highest proportion yet. Its head, who still has three permanent teaching posts unfilled, said it was easy to take on teachers as long as he was not concerned about quality.

“It is more difficult and more expensive than ever to recruit good teachers, or those prepared to take on any management responsibility,” he added.

A Kent head appointed five core subject teachers from America via telephone interviews. They all look good on paper, but with inspectors due in the autumn term she is hoping they are good in practice.

For one grammar school head, moving north has been the answer to his staffing problems. He has appointed seven permanent teachers to his North-west school, none of whom he has concerns about.

“As someone who has moved from the South-east from a selective school to a North-west selective, I can say that recruitment in my new school is significantly easier than at my former school.

“Posts in shortage subjects have been filled by excellent candidates. For a philosophy and religion post we shortlisted five Oxbridge candidates - three had 2:1s and two had firsts.”