The future of the government's health reforms has been plunged into fresh doubt as the Liberal Democrat peer Shirley Williams raises new concerns, and secret emails reveal plans to hand over the running of up to 20 hospitals to overseas companies. The revelations come as MPs prepare to return to Westminster on Tuesday for what promises to be a crucial stage of the flagship health and social care bill.

Baroness Williams, one of the original leaders of a Lib Dem rebellion against health secretary Andrew Lansley's plans – who appeared to have been pacified after changes were made over the summer – said she had new doubts, having re-examined the proposals. "Despite the great efforts made by Nick Clegg and Paul Burstow [the Lib Dem health minister], I still have huge concerns about the bill. The battle is far from over," she said.

Writing in Sunday's Observer, Williams raises a series of issues that she says must be addressed. Chief among them is a legal doubt as to whether the secretary of state will any longer be bound to deliver "a comprehensive health service for the people of England, free at the point of need".

Some critics of Lansley believe the Tories are bent on a mission to privatise the NHS, gradually handing it to the private sector. They fear that moves to end the legal obligation on the secretary of state to deliver comprehensive services may be a deliberate part of the process.

Concerns that ministers want more private involvement will be strengthened by details of email exchanges involving senior health officials about handing the management of 10 to 20 NHS hospitals to international private companies. The emails, which were made public following a freedom of information request and were obtained by non-profit-making investigations company Spinwatch, show that officials have been planning since late last year to bring in international companies. This is despite repeated insistences by both David Cameron and Nick Clegg that there will be no privatisation of the NHS. On 16 May, Cameron said: "Let me make clear: there will be no privatisation." Clegg said: "Yes to reform of the NHS, but no to the privatisation of the NHS."

One of the emails released by the department shows that officials at the private sector firm McKinsey, which advises ministers, were in active discussion about bringing in overseas firms to take over up to 20 hospitals in return for contracts running into hundreds of millions of pounds. An email to Ian Dalton, head of provider development at the Department of Health, who is heavily involved in the reform programme, in November last year talks about "interest in new solution for 10-20 hospitals but starting from a mindset of one at a time with various political constraints".

The emails show that McKinsey is acting as a broker between the department and "international players" that are bidding to run the NHS. The documents even lay out some of the conditions required by "international hospital provider groups" for running NHS hospitals. "International players can do an initiative if 500 million revenue [is] on the table." They also need to have "a free hand on staff management". The NHS would be allowed to "keep real estate and pensions".

The Department of Health attempted to play down the significance of the emails, saying they were referring to what might be done if any one hospital trust asked for the private sector to become involved in running a failing hospital. A spokesman said: "It is not unusual for the Department of Health to hold meetings with external organisations. Any decisions to involve organisations, such as the independent sector or foundation trusts, in running the management of NHS hospitals would be led by the NHS locally and in all cases NHS staff and assets would remain wholly owned by the NHS."

But a spokesman for the public service union Unison said: "Regardless of what Cameron and Clegg say in public, it is clear that behind the scenes the government is planning to privatise the NHS. Private companies will only run hospitals if they see a profit in it. This, together with lifting the cap off the number of private patients NHS hospitals can treat, will completely change the culture of the NHS. It will be profits before patients.

"We demand that the government come clean on their plans. If this is true, patient choice is a complete sham. The move to any qualified provider is clearly about creating a market for private companies. Any MP who votes for the health and social care bill is voting for the end of the NHS."

Williams also raises worries about the extent to which the role of the private sector is being expanded. "I am not against a private element in the NHS, which may bring innovatory ideas and good practice, provided it is within the framework of a public service …" she writes. "But why have they tried to get away from the NHS as a public service, among the most efficient, least expensive and fairest anywhere in the world? Why have they been bewitched by a flawed US system that is unable to provide a universal service and is very expensive indeed?"

She adds: "The remarkable vision of the 1945 Attlee government, of a public service free at the point of need for all the people of England, should not be allowed to die."

John Healey, Labour's shadow health secretary, said: "As David Cameron's government railroads the health bill through parliament, MPs are being denied their constitutional role to properly scrutinise his plans for the NHS. The prime minister has already done a political fix with Nick Clegg on the health bill, and now he's trying to force it through with a procedural fix."