The health secretary, Jeremy Hunt, has caved into pressure from doctors, Liberal Democrat ministers and Labour to rewrite regulations that would have increased private sector involvement in the NHS, just four weeks before they were due to come into effect.

Labour labelled the announcement that the regulations on competition in the NHS are to be overhauled a "humiliating U-turn" for the government, which has for nearly three years insisted that the Health and Social Care Act passed last year does not create privatisation by stealth.

The opposition and the Lib Dems were last night scrambling to claim credit for the promise to rewrite the whole of section 75 of the act, which covers the regulations introducing private competition into the health service that were published only last month.

Labour peers said the government was forced to act after they tabled a motion on Monday night that demanded the entire set of regulations be axed, something that posed a genuine threat to the coalition following government defeats over the original act in the House of Lords.

Lib Dem sources said the promised changes were secured after lobbying by their ministers, including a direct intervention by party leader Nick Clegg with David Cameron, but indicated that Hunt and the prime minister were receptive to the need to amend the regulations after the public outcry - including a petition signed by nearly 250,000 people.

Both sides of the coalition blame poor drafting of the regulations, published without the usual consultation with other ministers, rather than what critics claim was an attempt at "privatisation by the back door" of the NHS. A senior Lib Dem source said: "We did not feel [the regulations] were fit for purpose and would just generate confusion and concern."

Privatisation has been one of the biggest controversies in the coalition since the Health and Social Care Act was first published as a white paper a few weeks after the government was formed in 2010.

The latest row exploded last month when the detailed regulations in section 75 were finally laid before parliament. The new amended regulations will be published in the same way later this month.

Responding to an urgent question from Labour, Lib Dem health minister Norman Lamb told the Commons the government did not accept critics' claims that section 75 would allow wholesale privatisation of the NHS, but offered to rewrite parts of the regulations "to remove any doubt".

Sections being amended include clauses to make it clear that clinical commissioning groups (CCGs) of GPs who are due to shortly take on oversight of patient care will decide when and how competition should be sought; assurances that CCGs do not have to tender all services, and cannot be forced to by the regulator, Monitor; an insistence that competition must not be at the expense of "integration and co-operation"; and clearer rules about the exceptional circumstances when only one organisation can tender for a service without competition for the contract.

In all cases, the regulations would be based on standards adopted by the previous Labour government, when the now shadow health secretary Andy Burnham was in charge of the health department, said Lamb.

Burnham said that four weeks before CCGs were due to take over, coalition policy on competition was "in utter chaos". "It beggars belief that almost three years after the white paper and the upheaval inflicted on the NHS there's still no clarity on policy today."

Stephen Dorrell, Conservative chairman of the health select committee, said the government's clarification "demonstrates that the cloud of rhetoric that surrounded the passage of the Health and Social Care Act was so much hot air".

• This article was amended on Wednesday 6 March 2013 to include the updated version that was published in the Guardian newspaper.

