The dispute within the coalition government over NHS reformshas intensified after Nick Clegg demanded the removal of another main part of the proposals designed to encourage competition and private sector involvement.

The deputy prime minister has put himself on a collision course with the health secretary, Andrew Lansley, by proposing that a clause in the bill encouraging "any qualified provider" to take over services from the NHS should be radically rethought or dropped.

Clegg told senior Liberal Democrats that he would scupper Lansley's bill unless the Tories agreed to the new demand. He has already insisted on scrapping the requirement that Monitor, the NHS regulator, compels hospitals to compete with each other. He wants it to be replaced with a duty to promote collaboration.

Speaking at a meeting of his party's leadership – attended by Danny Alexander, chief secretary to the Treasury, Norman Lamb, policy chief, and Paul Burstow, health and social care minister – Clegg said: "Everybody accepts the need for reform, but nothing is more important to me than getting these reforms right.

"This should not be about imposing different providers from the top, but should be driven by what is needed by patients at the bottom."

The Lib Dem move will cause potentially unsustainable tensions in the government, where there is growing restlessness on the right of the Tory party about the posturing of their coalition partners over the health and social care bill.

Lansley's legislation is designed to encourage further involvement by the voluntary and private sectors by giving GPs the power to choose private healthcare for their patients over NHS hospitals. But amid growing concerns over potential privatisation, Liberal Democrats now want to offer protection from competition for NHS hospitals already struggling to make £20bn of savings, which Sir David Nicholson, the NHS chief executive, has demanded by 2015.

A party statement said: "We must drop the plans to introduce overnight a blanket policy of 'any qualified provider', as this risks destabilising too many providers [hospitals] at a time when they are having to make huge savings. Instead we should open up new services in a steady, phased manner, driven by patient demands."

At the meeting, the party leadership also rejected Lansley's bid to remove the health secretary's power to prevent the closure of hospitals. Clegg agreed to insist to the prime minister and Lansley that all healthcare providers, including private firms, should contribute to the training of doctors and nurses.

A Department of Health spokesperson said: "We are currently engaged in the listening exercise and we have said where there are good suggestions to improve the legislation, those changes will be made. We await the recommendations from the NHS Future Forum, expected early next month."

The dramatic development came as a survey of the country's leading private healthcare companies showed that four out of five chief executives believed that the current NHS reforms would provide an opportunity for them to profit.

Parthenon Group, a strategic consultancy that interviewed the chief executives, found that companies either believed that they would benefit by taking over services now monopolised by NHS hospitals, or that government policy would starve the NHS of funds and drive more people to take private insurance or "self-pay" – abandoning free care to go private.

According to the survey, the overwhelming majority of the companies said that they were planning to spend more on marketing aimed at GPs, who will have the power of commissioning under the reforms, and at patients to boost the profile of their "brands". The survey was seized on by critics. John Healey, the shadow health secretary, said: "This exposes the truth at the heart of the Tories' NHS plans. The big winners will be private health firms, not patients. These companies are not waiting about – they are already hard-selling their services into the NHS."

Last week the prime minister was accused of trying to privatise the NHS after the Observer revealed that Mark Britnell, invited to Downing Street to provide advice earlier this month, had told a conference in New York that the NHS would be shown "no mercy" and would become a "state insurance provider rather than a state deliverer".

Cameron subsequently distanced himself from Britnell, an executive at accountancy giant KPMG, claiming not to have heard of him, although it later transpired that the health expert had been the chief executive of the strategic health authority serving the prime minister's constituency when he was campaigning to have a new hospital built.