Britain is fast becoming a Third World country because of a failure to educate the next generation of scientists and engineers, independent schools warned today.
Jonathan Shephard, general secretary of the Independent Schools Council, said ministers would have to work with private schools to turn the situation around.
Countries such as India and China are producing tens of thousands of engineering graduates and mathematicians every year while numbers on these courses in the UK have plummeted, he said.
Speaking to reporters at the Headmasters' and Headmistresses' Conference in Sutton Coldfield, West Midlands, Mr Shephard said: "We have to start talking to the Government as partners in UK educational provision.
"Despite a number of improvements in state (school) results, the decline in maths, sciences, engineering and modern languages is insupportable and has to be reversed."
Private-school heads clashed with Jacqui Smith, the schools minister, who was adressing the conference instead of Ruth Kelly, the Education Secretary, who was originally billed to appear.
She rejected calls from them to introduce education vouchers or assisted places, the programme scrapped by Labour in 1997 in which taxpayers contributed to the private-school fees of poor children.
"You have called for assisted places, but I don't believe in a system where only a few are given the keys to the room at the top," she said. "Isn't the answer to ensure that excellence and challenge wherever it comes from is drafted into the state system, rather than provide a few with an escape route out?"
The minister insisted that the best way for private schools to display their "public benefit" - a key element of the forthcoming Charity Bill, which will decide whether or not they retain their charitable status - was for more partnerships to emerge between state and private schools.
There were also clashes within the private-sector world with Priscilla Chadwick, chair of the HMC, accusing companies of offering low-fee private education while making a "quick buck at parents' expense".
The organisation represents 246 of the UK's most expensive private schools, including Eton and Harrow. She said some firms were maximising profit by increasing class sizes and offering a limited curriculum.
Global Education Management Systems (Gems) and Cognita, the private education firm run by Chris Woodhead, which have both pledged lower fees compared with the rest of the sector were obviously the firms within her sights.
Dr Chadwick said parents should not be fooled by "the rhetoric of schools established for shareholders' profit, which cut back to basics while making a quick buck at parents' expense".
Professor Woodhead, former chief inspector, later responded by saying that the curriculum offered by his 22 schools has not been altered since they fell into Cognita's hands.
Dr Chadwick's comments came as it emerged that Gems, which owns 13 schools in England, has failed in its bid to buy into the state sector for the first time.
The company, which pulled out of a deal earlier this year to sponsor an academy, announced last November that it was on the verge of purchasing 3E's, a company with contracts to manage state schools.
But Valerie Bragg, 3E's founder, told The TES this week that it had rejected Gems' advances, even though the Dubai-based firm had already placed the 3E's logo on its website.
HMC has indicated that it may set up its own exams and professional qualifications amid continuing concern over standards elsewhere in the education sector.
Geoff Lucas, HMC secretary, said some private schools were in discussions with the OCR exam board with a view to creating new examinations following a lack of confidence in A-levels.
Dr Chadwick said that HMC would be conducting research into the possible launch of its own national professional qualification for headship (NPQH) and teacher training.