The government has lost a House of Lords vote on its controversial plans to overhaul the NHS in England.

The first of those debated on Wednesday – demanding that the health secretary ensures that mental health care is treated as importantly as physical health care by the NHS – was put forward cross-bencher Lord Patel, and passed by a by 244 votes to 240.

Three Liberal Democrats – Lord Alliance, Lord Carlile of Berriew and Baroness Tonge – rebelled against the government.

Peers accepted a government-backed amendment specifying that the health secretary retains "ministerial responsibility to Parliament for the provision of the health service in England".

Several more amendments – all discussing the powers and responsibilities of the health secretary – were debated.

Opposition to the bill from medical professionals – including the British Medical Association and the Royal College of Nursing – has led to speculation about Health Secretary Andrew Lansley's position.

At prime minister's questions in the House of Commons, Mr Miliband told Mr Cameron: "You know, in your heart of hearts, this is a complete disaster, this bill."

Referring to a critical article on the Tory Reform Group website saying: "It comes to something when even the Tories don't trust the Tories on the NHS."

He said the prime minister had broken a pre-election promise not to have any "top-down re-organisation of the NHS" and told him: "Every day he fights for this bill, every day trust in him on the NHS ebbs away, every day it becomes clearer the NHS is not safe in his hands."

But Mr Cameron said Labour had previously supported NHS reform – and would not match government commitments on NHS spending: "They are not in favour of the money. They are not in favour of the reform. They are just a bunch of opportunists."

He criticised Labour's record on the NHS in Wales – where the party controls the Welsh Assembly – and said the coalition was cutting bureaucracy and ploughing money back into patient care.

He said of Mr Miliband: "This is not a campaign to save the NHS. This is a campaign to try and save his leadership. I make this prediction, the NHS will go on getting better and his prospects will go on getting worse."

The Tory Reform Group later accused Mr Miliband of a "complete misrepresentation" of its position – as the blog post had been written by an independent contributor and it said it remained a "staunch supporter" of the proposals.

As the session was under way in the Commons, the Faculty of Public Health became the latest healthcare body to call for the Bill to be dropped, "in the best interests of everyone's health".

But 54 NHS Trust directors backed a provision in the bill to allow hospitals to raise up to 49% of their income from private patients, saying in a letter to the Times, that there were "sound medical and clinical reasons" for it.

On Tuesday Downing Street said Mr Lansley had the prime minister's "full support" – following an anonymous quote in the Times, attributed to a Downing Street source, suggesting the health secretary should be "taken out and shot" over the policy.

It was even suggested that the former Labour Health Secretary Alan Milburn might be given a peerage and then take over from Mr Lansley.

But Mr Milburn told BBC Radio 4's World at One there was "fat chance" of that happening.