• Tories down four points to 36% in latest Guardian/ICM poll • Labour up one point on 37%, Lib Dems down two on 14% • Majority of respondents (52%) want NHS bill dropped

David Cameron has squandered the Conservatives' new year lead as voters turn against his health reforms, according to a Guardian/ICM poll. The Tories are down by four percentage points in a single month, slipping from 40% to 36% since January.

Labour is one point ahead, on 37%, with Ed Miliband's party up from 35% last month. The Liberal Democrats slip back two to stand at 14%, and the combined total of the smaller parties has climbed by four points, to 13%.

As the prime minister hosted a special NHS summit, which excluded the professional bodies most opposed to his health and social care bill, the public is siding with those royal medical colleges who want the legislation ditched.

An outright majority of respondents, 52%, say that the bill – which would overhaul NHS management, increase competition and give family doctors more financial responsibility – should be dropped. That is against 33% who believe it is better to stick with the plans at this stage.

The 19-point overall margin in favour of abandoning the legislation is mirrored in strong leads for killing the bill across all social classes and regions, as well as among male and female voters.

Only the very youngest respondents aged 18 to 24, the least likely to vote, favour sticking with the plans, by 46% to 39%. Opposition hardens with age, and is at its most marked among the over-65s – who favour dropping the bill by a 56% to 29% margin. A third of Conservatives (31%) and a significant majority of Lib Dem voters (57%) also want the proposed law to be ditched.

With crunch votes on the drive to extend medical competition likely to take place in the House of Lords next week, the role of the private sector in the health service is becoming more controversial. Even though respondents were reminded that private companies already provide some NHS treatments, a clear majority, 53%, believe that such competition undermines the health service, compared with just 39% who believe it forces the NHS to raise its service standards.

When ICM asked a slightly different question on private involvement in September 2005, at the height of the controversy about Tony Blair's NHS reforms, opinion was evenly split – with 48% in favour of more private involvement, and 49% against.

There are signs that the Conservatives' failure to persuade the public about its NHS reforms could contribute to a "retoxification" of the Tory brand. Cameron – who once said his priorities could be summed up in the three letters "NHS" – initially invested a great deal of effort in overcoming the Conservatives' historic difficulties on the terrain of health.

One year into his leadership, ICM found he had made progress – in October 2006 only 31% said they did not trust the Tories at all to run the health service, as against 32% who said the same of Labour. In the latest poll, however, 40% of respondents said they did not trust the Conservatives at all, against 25% who say the same about Labour.

Only a minority of voters trust either of the main parties "a lot" on the health service – 23% for Labour, and a mere 13% for the Conservatives. Labour is trusted "a little" by 46% of respondents, while 42% say the same of the Conservatives.

Lib Dems will be especially interested in the results of the poll. The party's peers could provide the decisive swing votes to amend the health bill in the Lords, and – with many of the party's activists anxious about the reforms – the NHS is expected to loom large at its spring conference next month.

The junior coalition partner can point to a series of concessions it has wrung out of the Conservatives since last year's "pause" in the legislation's progress, but the public does not seem to have noticed.

Just 9% trust the Lib Dems a lot on health, against 45% who trust them a little and 39% who do not trust them at all, figures that are strikingly similar to those for the Tories.

By 50% to 46%, remaining Lib Dem supporters are inclined to believe that competition can spur the NHS to raise its game. But among the larger group who backed the party in the 2010 election, the predominant view is that competition will instead undermine the health service, by a two-to-one margin of 60% to 32%. Dropping the bill would be especially popular among 2010 Lib Dem voters, with 67% of them backing that option, as against just 21% of this group who want the government to stick with its plans.

ICM Research interviewed a random sample of 1,013 adults aged 18+ by telephone on 17-19 February 2012. Interviews were conducted across the country and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.