Less than a third of people support plans to allow private companies to provide NHS services, according to an influential survey.

The opinion poll by YouGov – the first of its kind to gauge opinion on the controversial shakeup – suggests that a recent push by ministers to sell the plans has fallen largely on deaf ears.

The findings come as MPs prepare to debate the health and social care bill in parliament on Monday. The bill paves the way for GPs to take on the role of commissioning health care and for the private sector to expand its role in the provision of NHS services.

Tonight, after one Liberal Democrat MP organised a public meeting to highlight what he sees as the potential dangers of the plans, shadow health secretary John Healey appealed to members of Nick Clegg's party to oppose the bill in parliament.

The YouGov survey found that only 27% of people back moves to allow profit-making companies to increase their role the NHS.

The health secretary, Andrew Lansley, plans to allow groups of GPs in England to commission £80bn a year of care for their patients after April 2013 from "any willing provider".

Overall, 50% of the 1,892 respondents opposed the policy. But hostility was more evident among Lib Dem voters, 56% of whom said they were against, with just 30% in favour. Conservative supporters were also split: while 46% backed the use of private firms, 32% were against.

In recent weeks Lansley and other ministers have mounted a huge publicity drive to sell the reforms, after being criticised for failing to put their ideas to voters before the general election. But Dave Prentis, general secretary of public services union Unison, which commissioned the poll, said the findings showed the true depth of hostility.

"There is very weak support from Tory voters and clear opposition from Lib Dems," he said. "There is very little support for this bill anywhere. Many GPs are opposed to it, as are patients, NHS staff, clinicians, charities, thinktanks, MPs and unions. Lansley's vanity project is undemocratic, unaffordable and unnecessary."

A Department of Health source said: "We want patients to be able to choose to be treated wherever they want, whether it's an NHS hospital or in the voluntary or private sectors. More choice and more competition will lead to benefits for patients. Labour introduced this policy in 2007 and since then the number of patients choosing an independent provider has risen to more than 16,000 a month. But, unlike Labour, we won't pay the private sector any more than we would pay the NHS. And we will establish a powerful new regulator to enforce these rules."

Dr Clare Gerada, who chairs the Royal College of GPs, said: "The RCGP is keen to ensure that the reforms work for patients and the NHS. The RCGP is concerned that the policy of 'any willing provider' could lead to fragmentation and duplication."

The poll also reveals that half the public oppose the new GP consortiums that will emerge across England, using private management groups to help them with finance, planning and management. Lib Dem voters are even more hostile to this, with 57% against, while among Tory voters, 40% back it with 38%against.

"The lack of support is unsurprising, given that people were not told before the election about these plans for a high-cost, high-risk reorganisation of the health service," said Healey. "But it is also now clear that even committed Conservative voters are not convinced the government is making the right decisions for the NHS."

In a letter to all Lib Dem MPs, Healey said the ideas being promoted by Lansley were out of line with their party's beliefs and previous policies.

On Friday the Lib Dem Andrew George, MP for St Ives, Cornwall, urged the public to attend a meeting in his constituency to discuss the reforms. George said: "These changes are fundamental. They go to the heart of the origins of the NHS. Because so much will be happening at once, I don't think that local people fully appreciate what might happen and the risk and challenges ahead."