Officials at the Department for Education and Employment accept that the target cannot be reached without taking in more schools or opening the scheme to children as young as eight.

According to a Government source, the possibility of offering assisted places to younger children will be investigated if independent schools do not offer substantial numbers of additional places for 11 to 18-year-olds.

There are already 295 independent schools in the scheme and there are doubts as to whether there are many others with the academic requirements wanting to take part. Schools have to be able to demonstrate excellent exam results; have a sixth-form of at least 60, and have to be teaching Latin or Greek to at least GCSE level.

Tony Edwards, professor of education at Newcastle University and one of the authors of the definitive research on the scheme, believes expansion would present great difficulties without diluting the scheme’s scholarship nature or widening the age group.

“When the scheme was first announced in 1981, a significant number of schools applied that could not meet the requirements. The addition of a further 50 schools in 1987 was not accomplished with ease. I can’t believe there are large numbers of schools eligible and willing to join the scheme,” he says.

However, the DFEE press office insisted there had been enquiries from more than 100 schools, but the press office refused to give any names on the grounds that would imply they had Government approval.

Two schools known to be interested are St Edmund’s in Canterbury and Birkdale in Sheffield - both have applied in the past.

The schools that have substantial numbers of pupils on assisted places say they do not envisage taking many more next September. Almost 40 per cent of pupils at Wolverhampton Grammar have their fees at least partially met through the scheme. However, the head, Bernard Trafford, believes he could only add another 10 to the 40 11-year-olds he plans to take in the next academic year.

“The numbers depend on supply and demand. We are not turning away lots of potential assisted places pupils. We might manage another 10,” he says. Like other schools, Wolverhampton says the Government is forcing them to subsidise assisted places by not paying the full cost of educating children on the scheme. For the last three years, the assistance has only been increased in line with inflation and schools claim that as a consequence they have had to charge fee payers more.

At Dulwich College, which has 269 pupils on assisted places,the acting master, Christopher Field, said the school would probably seek a limited expansion of places for 11-year-olds. However, he added, the governors would have to examine whether the school should increase its dependency on a scheme that was vulnerable should there be a change in government.

The prospect of assisted places lower down the age range has been welcomed by Chris Evers, chairman of the Incorporated Association of Preparatory Schools. “If the scheme is extended, it will provide the opportunity for bright children to enjoy a prep school-type education,” he says.

However, ministers may be wary of accusations that they are providing extra funds to the private sector at a time when state primary schools are having to increase the size of classes.