An attempt to strip abortion providers of their role in counselling women was heavily defeated in the House of Commons this afternoon after a split between the original supporters of the amendment.

MPs voted by 368 votes to 118 – a majority of 250 – to reject the amendment by the Tory backbencher Nadine Dorries after she lost the support of her co-sponsor, the former Labour minister Frank Field.

Dorries managed to win the support of three cabinet ministers – Iain Duncan Smith, the work and pensions secretary, Liam Fox, the defence secretary, and Owen Paterson, the Northern Ireland secretary.

Field withdrew his support for the Dorries amendment after Anne Milton, the health minister, said the government would try to implement the spirit of her proposal.

Milton told MPs: "The government is … supportive of the spirit of these amendments and we intend to bring forward proposals for regulations accordingly, but after consultation. Primary legislation is not only unnecessary but would deprive parliament of the opportunity to consider the detail of how this service would develop and evolve."

Dorries hailed Milton's undertaking as a victory. She told the BBC's Norman Smith: "We lost the battle but we have won the war."

Milton distanced the government from the amendment towards the end of a scratchy debate in which Dorries said that David Cameron had initially encouraged her.

Dorries claimed that the prime minister had advised her on the wording of her amendment by saying that she should describe abortion counsellors as independent.

Dorries said: "I went to see the prime minister regarding this amendment and he was very encouraging. In fact it was at the prime minister's insistence that I inserted the word 'independent'. I attended a meeting at the Department of Health and at that meeting it was decided what the outcome, the process that would be implemented, to make this a reality."

The Dorries amendment would have stripped non-statutory abortion providers such as Marie Stopes and the British Pregnancy Advisory Service (bpas) from offering counselling to women. This was designed to provide greater opportunities for independent counsellors, some of whom are influenced by pro-life groups, to provide counselling. NHS abortion providers would still be free to offer counselling.

Dorries claimed that the prime minister changed his mind under pressure from Nick Clegg, after the deputy prime minister was lobbied by the former Lib Dem MP Evan Harris. Dorries said: "Basically the Liberal Democrats, in fact a former MP who lost his seat in this place, is blackmailing our prime minister. Our prime minister has been put in an impossible position regarding this amendment. Our health bill has been held to ransom by a former Liberal Democrat MP."

A senior Lib Dem source dismissed her allegation. The source said: "That is utter rubbish. [Nick] doesn't need Evan to tell him the problems with her amendment."

The defeat was welcomed by bpas. Ann Furedi, its chief executive, said: "Bpas is pleased to see Nadine Dorries's amendment so overwhelmingly rejected. We look forward to being able to focus our efforts on the issues which pose a genuine problem for women considering ending a pregnancy."

Dorries insisted that she did not want to restrict access to abortion. "I do not want to return to the days of back-street abortionists," she said. "I am pro-choice. Abortion is here to stay."

The MP said that it was wrong for abortion providers to counsel women with unplanned pregnancies. "It must be wrong that the abortion provider, who is paid to the tune of £60m to carry out terminations, should also provide the counselling if a woman feels strong or brave enough to ask for it. If an organisation is paid that much for abortions, where is the incentive to reduce them?"

Diane Abbott, the shadow public health minister, said: "This amendment is a shoddy, ill-conceived attempt to promote non-facts to make a non-case – namely that tens of thousands of women every year are either not getting counselling that they request or are getting counselling that is so poor that only new legislation can remedy the situation. In matters of this kind, if legislation is the answer then you have almost certainly asked the wrong question."