An NOP survey, commissioned by The Ramblers' Association, found 83 per cent of adults supported a backbench Bill to force landowners to open up about four million acres, The Independent can reveal.
The poll of 1,001 people throughout the UK shows that the proposals published last week by Gordon Prentice, MP for Pendle, attract overwhelming support across all ages and social classes. The legislation would allow the public freedom to walk on designated areas of mountain, moorland, heath, down and common land, subject to "common sense" restrictions to protect crops and animals.
NOP found that just 13 per cent believed their local MP should not back the Bill, compared with 83 per cent who wanted them to vote for it and 5 per cent who didn't know.
Support was strong in areas of dale and moorland where the measures would have most impact, with residents in Scotland, the North East, North West and Yorkshire all backing the idea by at least 79 per cent.
The Bill will receive its Second Reading next month and Labour MPs are anxious that it gets the government backing needed to ensure its passage.
Michael Meacher, the Environment minister, will publish his own proposals in the next few weeks, but they are expected to recommend voluntary agreements between landowners and councils to increase access.
By contrast, the Prentice Bill would honour Labour's manifesto commitment to give walkers a statutory freedom to roam by imposing big fines on landowners who do not comply.
The Bill is becoming known as the "John Smith Memorial Bill" in recognition of the pledge by the former Labour leader to introduce a right to roam; the issue has a strong emotional pull on the Parliamentary Labour Party.
More than 140 MPs, including four ministers and two former cabinet ministers, are likely to back the proposals. Many are furious at speculation that the Government will kill the Bill by refusing it parliamentary time.
Mr Prentice said last night that the poll result proved the popularity of the Right to Roam issue.
"The Government is faced with a stark choice: it could go along with the leaks published in the press recently that it will hand landowners a veto over access, or it could back legislation such as mine," he said.
"We have been relying on landowners offering voluntary access... for over 50 years, with little to show for our patience."