Tony Evans, chairman of the Headmasters’ and Headmistresses’ Conference, said it would be “an act of political vandalism which would force independent schools, totally against their will, into a divisive and unnecessary social enclave”.

The mood of the annual meeting of the HMC held in Glasgow this week was in marked contrast to last year’s when leaders were optimistic of a new relationship with the opposition party. Vivian Anthony, secretary of the HMC, said: “It’s fair to say we got on very well with David Blunkett [the shadow education secretary] and we got the impression that they were being serious about wanting to work with us.”

Mr Evans claimed that the money saved from abolishing the scheme would amount to only one 16th of a place at a primary school. Stephen Winkley, head of Uppingham School in Leicestershire, said abolition was “purely ideological, my daughter is in a class of 35 and the peanuts they’ll get from doing away with the APS won’t make any difference to her”.

Michael Mavor, head of Rugby School and chairman-elect, thought that schools would not suffer, but pupils would. “It’s a shame for the country as a whole.”

The Independent Schools Information Service will soon be mounting a campaign to remind parents of the benefits of the scheme and alert them to its possible demise under Labour. A poll carried out by ISIS in August showed that more than half the people intending to vote Labour supported the APS.

Shortly after last year’s conference, the Government announced a doubling of of the scheme from the current 34,000, depending on parental demand and the supply of high-quality places.

Speakers were also concerned with issues of moral and pastoral education, but were reassured by Mr Evans that schools should not be blamed for society’s inconsistencies and conflicting values. “Schools do not give away a crate of yob-labelled ‘alcopop’ with every registration.”

Stark evidence of coping with family breakdown was given to the 300, mainly male, delegates, by guest speaker Lee Palmer-Jones, head of Brackenhoe School, a local-authority run comprehensive, in a severely-deprived area of Middlesbrough. More than half of her 570 pupils are on free school meals, many have special educational needs, most are smaller than average and are two years behind in emotional and physical development. Half were from single-parent families and many did not know their fathers.

Despite political assertions to the contrary, research shows there is a correlation between poverty and deprivation and low educational achievement, she said.

Mrs Palmer-Jones, who is area president of the Secondary Heads Association, said fellow inner-city heads were increasingly worried about pupils becoming victims of drug-pushers. Youngsters turned to crime or prostitution to pay off debts. One Humberside head told her that the situation was in “meltdown”.

She said:“Nobody seems to be interested in schools at the bottom of the league tables which just pour further humiliation on them. Some parents can’t express a preference for a school - they probably can’t afford the bus fare. But their children do need an education.”