Just 10% of people trust the views of the prime minister and health secretary more than organisations representing health professionals on NHS reform, the poll found.
The poll, by YouGov for Progressive Polling and the health union Unite found that 59% of 1,772 people who took part believed the prime minister had failed to deliver on his promises about the NHS in the last general election.
A total of 43% of respondents now believe Labour has the best policies on the NHS, compared with 28% for the Conservatives.
The poll also found that 68% of people believe the government should make public a risk register it has refused to publish, setting out concerns about the impact of NHS reforms.
The responses were weighted to be representative of the adult population of Great Britain.