Dr Bernard Trafford, who takes over the chairmanship of the Headmasters' and Headmistresses' Conference tomorrow, said private schools were concerned about increasing competition from the independent state schools.
The impressive new facilities and degree of freedom that academies enjoy could prove attractive to parents, he said.
"There is a lot of talk from the Government about independence. We are in danger of having that word stolen from us," said Dr Trafford.
"We need to reassert what our independence means. The Government copying what we do is flattering, but for some of our schools, academies could be a real problem. They feel threatened by a beautiful new pound;40 million building opening down the road from them because it is competition. The only answer is for us to be really good."
Two independent schools, William Hulme's Grammar in Manchester and Belvedere in Liverpool, will become academies in September.
As revealed in The TES, more than 30 independent schools, including members of the HMC, could follow suit. It is expected to appeal to schools struggling to attract enough full fee-paying pupils.
A number of other private schools, including Wellington College in Berkshire and Dulwich College in south London, plan to sponsor academies.
Dr Trafford, who is head of Wolverhampton Grammar, said the issue of academies would be debated over two days at the HMC annual conference in October.
"I don't have a personal agenda about them either way, but we need to air the issues. I expect there might be some arguments about them," he said.
The HMC represents 250 leading schools, including Eton College, Harrow school and Winchester College.
Fees at independent schools rose by 6 per cent last year above the rate of inflation and by more than 40 per cent in the past five years.
Debate about A-levels, the International Baccalaureate and the Cambridge Pre-U exams will be hot topics at this year's HMC conference, Dr Trafford said.
he jury was still out on the Pre-U, designed to offer a more traditional alternative to A-level.
Schools are waiting for a clearer indication from universities about how they will treat the qualification before deciding whether to use it, he said.