His local authority has received the minimum, 3.2 per cent, funding increase. But he believes the needs of his school, such as acute staffing shortages, have been overlooked because the Government has based its calculations on “crude indicators” of the area’s general prosperity.

“The Government assumes that the areas of need are those in urban locations. But it is not simply a question of metropolitan area versus rural shire, or north against south,” he said.

“It has not taken account of the fact that relatively affluent counties such as ours also have underprivileged pockets where children are in danger of becoming a forgotten underclass. People may think of this as a nice, leafy area, but we still have patches that are socially deprived.

“And because Buckinghamshire, like Kent, is a selective authority, it means that children from disadvantaged backgrounds are concentrated in a small number of secondary schools.”

Staff at schools in the south of the county, including Amersham, benefit from London fringe allowances, but those in other parts of the county do not qualify for any extra allowance, even though house prices are comparable to parts of London.

Mr Edgar said: “Schools are relying on a growing number of expensive agency staff and we are spending money on trying to recruit from foreign countries. We are also losing secretaries and other support staff to the commercial sector, which is able to offer wages that reflect the cost of living in Buckinghamshire.”

Secondary modern schools in the county already have a funding gripe. Twelve of Buckinghamshire’s 21 upper schools are in deficit with the group collectively pound;1.1 million in the red. The 13 grammars are much better off: together they have nearly pound;2 million in the bank.

Campaigners against selection in the county say that they are not challenging the 11-plus system, but also the differential funding.

They are using a report commissioned from a London university academic to back their claims for more cash.

The upper schools say they miss out on cash because of the way that Buckinghamshire delegates funding to schools.

The funding per post-16 pupil is relatively generous, which benefits the grammar schools with their large sixth forms, while funding per special needs pupil is below average - penalising the upper schools, which have more such children.

The council also spends pound;3.5 million more than typical on school transport, mainly on bussing grammar pupils to school.