Vote may 'skew' perception of coalition priorities says No 10 insider, with polls also suggesting it would be unlikely to succeed

David Cameron is likely to postpone a free vote on lifting the ban on hunting with dogs indefinitely in the face of overwhelming evidence that the ban would be retained if MPs did vote, and that a vote might possibly tighten the current law.

A free vote will also irritate Liberal Democrats, with 42 of the 57 Liberal Democrats MPs opposed to lifting a ban, including the party leader, Nick Clegg.

A commitment to a free vote is in the coalition agreement but is not seen as a priority given bigger issues relating to the economy and public services.

A Downing Street source said a vote would also look like a skewed sense of priorities, and remind some voters that the coalition can be seriously divided on social issues.

Cameron, a self-confessed "shire Tory", has said he is a country man at heart and favours hunting, but he recognises it is a highly divisive issue and would play to negative stereotypes around his party.

Coalition members are aware that a free vote, as Tony Blair discovered, can swallow a huge amount of parliamentary time and energy. The 2004 Hunting Act convulsed the second term of the Labour government and exasperated Blair, leading him to admit in his autobiography the ban was a mistake based on ignorance.

The farming minister, James Paice, confirmed on Friday that lifting the ban was not a legislative priority for him, or for the department of environment, food and rural affairs.

A comprehensive survey of MPs conducted by the League against Cruel Sports last month showed any repeal of the Hunting Act would be defeated by 310 votes to 253, with 23 MPs undecided. A total of 42 Liberal Democrats MPs would oppose lifting the ban, leaving advocates of repeal heavily dependent on Conservatives. There are now 22 Conservative MPs who oppose repeal, including some new members. Five new Tory MPs, including Caroline Dinenage, Mike Weatherley and Tracey Crouch, backed a statement issued at the weekend saying that "this government has far more important things to do than spending time on bringing back cruelty to animals for sport".

Some Tory MPs oppose lifting the ban because they believe the current legislative position allows many hunts, in practice, to continue to chase foxes and remain inside the law. It is likely that legislation would be promoted only if Cameron felt it necessary to re-engage an enthusiastic countryside vote ahead of a general election. But even then the issue is likely to alienate some centrist Tories.

A survey by Ipsos-Mori for the League Against Cruel Sports released on Boxing Day showed that 76% of the British public think fox hunting should remain illegal, while 84% think stag and hare hunting should also remain illegal. Only one in six, 18%, think fox hunting should be legalised again, with only one in 10 thinking hare hunting and coursing should be made legal. Seven in 10 rural dwellers think fox hunting should not be legalised.

Conservatives Against Fox Hunting, a recently formed campaign group, claims that two-thirds of Conservative supporters oppose any repeal.

Louise Robertson, of the League Against Cruel Sports, said she was confident there is no public appetite for repealing the act. She said the league had polled every MP on the issue and it was "very firmly stacked against repeal". She said contrary to what the Countryside Alliance said, there had been 57 prosecutions for illegal hunting.She claimed that a large number of hunts were not hunting within the terms of the act and the number of prosecutions was increasing year on year. If the dogs were not controlled properly and chased and killed a fox, that was illegal.

The Countryside Alliance has produced a poll of more than 1,000 people, carried out by ORB, showing two-thirds of people agree that the hunting ban and the time spent enforcing was not a good use of police resources.

The Countryside Alliance's chief executive, Alice Barnard, said the act has "wasted thousands of hours of police time and millions of pounds of taxpayers' money". When repeal was debated, she said, the alliance was confident the country and parliament would support the arguments for ending the ban.

Today was supposed to be the biggest day of the hunting calendar, but snow and ice made conditions for riders too dangerous in many areas and some of the 300 hunts scheduled to take place were cancelled.