Carole Evans, headmistress of Birkenhead high school in Merseyside, which charges up to £6,000 a year, warned that plans being considered by the government for a big increase in tuition fees would put people off university.
Mrs Evans, who is also the president of the Girls' School Association, said: "In my school it would have an effect, because a lot of girls are there on a free place and come from families who have no background in higher education.
"They are first-time buyers into higher education. There are a lot of families for whom acquiring debt is something they cannot tolerate."
She added: "I think higher education should be available to any pupil who is able to benefit from that education, regardless of their background."
One of the arguments used by advocates of top-up fees inside and outside the government is that many middle-class parents - covering 7% of the school population - already pay sustantial fees for their children's school education. Some academics have also called on the government to introduce an extra tariff to make students who have been to private school pay more at university.
Mrs Evans was backed by other heads at the opening of the association's annual conference in Manchester.
Sarah Evans, headmistress of King Edward VI high school for Girls in Birmingham, said: "We feel that higher education is underfunded, but the additional funding for higher education should come through the tax system." The govern ment should further explore the option of a graduate tax, which students paid once they left university.
Pauline Davies, headmistress of Wycombe Abbey school in Buckinghamshire, where fees are nearly £15,000 for day pupils and more than £18,000 for boarders, said that some parents would no longer be able to afford school fees if they had to pay more for university education.
"Many parents in the independent sector already make significant sacrifices to make that choice in the best interests of their children," she said.
The heads also criticised the government's target of having 50% of young people entering higher education by 2010 - not because it was too high, but because they believed it had no rationale.
"Why not 60% or 75%? Anyone who can benefit from higher education should be able to access it," Mrs Evans said. In her opening speech to conference she urged ministers to reject proposals, being considered in the ongoing review of higher education, to reward universities which took on greater numbers of state school pupils.: "The government has benchmarks showing the number of students from each sector for which universities should aim. We must ensure that these benchmarks do not become linked with finance and in effect become quotas."
Mrs Evans accused the government of failing to live up to its promises of partnership with the independent sector, repeated recently by the school standards minister, David Miliband.
Private school teachers had been denied the chance to bid for money for information technology training, and the government would not repay student loans for teachers in the independent sector as they did for those in state schools.
"We must question whether this government's oratory over partnership will ever be matched by action."
