More than two out of five people fear the NHS will cease to be a free service over the next 20 years, a new survey reveals. When asked how likely it was that the NHS by 2034 would still be free at point of use, 44% said it was unlikely and 37% thought it was likely to be the case.

Women and the less well-off were the most pessimistic. Among women, 48% believe the free NHS will have disappeared, while 36% do not. More men (40%) share that concern, though almost as many (38%) think free care will survive.

The findings, from a survey of 1,030 adults in England by pollsters Populus, come after several thinktanks, groups of health professionals and ex-Labour health minister Lord Warner said the NHS should introduce charges, notably for visiting GPs, as a way of reducing the burden on the taxpayer.

The survey, undertaken before NHS England this week sets out its radical plan to save the service, also found low levels of voter trust in political parties to put the NHS’s growing problems ahead of their own self-interest. Labour again emerged as the party that most voters (47%) trust on the NHS, followed by the Conservatives (38%), Liberal Democrats (35%) and Ukip (32%). Fifty-two percent did not trust either the Tories or Lib Dems on the NHS.

James Tyrrell, director of Insight Public Affairs, which commissioned the survey, said the results revealed widespread anxiety about the NHS’s future despite the parties recently making high-profile pledges to give it extra funds in 2015-20. “The public are worried about our NHS, about how it’s funded and the services it can provide. It’s clear that political parties working on their own aren’t trusted to keep the NHS on a lomg-term sustainable footing.”

A separate survey, by YouGov for the NHS Confederation, found that a surprisingly high number of people – 76% – would back changes to NHS services if they believed that would improve the quality of care. The findings may be an indication that the centralisation of some hospital services could meet with less resistance as long as it is well explained.