Most voters in key battleground constituencies want to see the NHS safeguarded from a new trade deal which campaigners claim threatens privatisation of health services, according to a new survey.

More than two-thirds opposed the inclusion of the NHS in negotiations over the Transatlatic Trade and Investment Partnership, a poll of more than 2,600 adults in 13 marginal Conservative constituencies for the Unite union showed.

Opponents claim the trade deal is being negotiated behind the closed doors of the European Commission between EU bureaucrats and delegates from the US.

The government denies any deal will lead to the privatisation of the NHS, saying it would create jobs.

Unite general secretary Len McCluskey said: “The Tories’ Health Act of 2012 opened our NHS up to profit making US private firms and a new trade deal threatens to make the sell-off permanent. It’s clear from this poll that the NHS is going to be a major issue at next year’s election.

“The results prove that people firmly oppose the inclusion of the NHS as part of the trade deal. A majority of people even think that David Cameron should use Britain’s veto.

“David Cameron’s silence is deafening. He is refusing to answer a very simple question: are we going to exempt health from the EU US trade agreement?

“Unless he acts, the NHS will be at the mercy of US companies and Wall Street investors who will be able to sue the government in secret courts if it tries to reverse privatisation.”

Damian Lyons Lowe, chief executive of Survation which conducted the survey, said: “When the potential implications of this trade deal are put to voters, they are clear that protecting the NHS is of paramount importance, notwithstanding the benefits of a trading partnership.

“As this poll shows, healthcare is an issue that cuts across political divides and so may prove critical to MPs in marginal constituencies sitting on very small majorities. Should public awareness become widespread, this could, based on our polling, become an electoral liability for David Cameron if he does not heed public concerns.”

The constituencies where the polling was held were Amber Valley, North Warwickshire, Broxtowe, Lancaster and Fleetwood, Brighton Kemptown, Lincoln, Morecambe and Lunesdale, Sherwood, Thurrock, Cannock Chase, West Dorset, Camborne and Redruth, and Truro and Falmouth.

 A Department of Health spokesman said: “We have no intention of allowing the [partnership] to dictate the opening up of NHS services to further competition; and it will not do so. The NHS will always be free at the point of use for everyone who needs it.”