Fewer than one in five people in the UK would support a repeal of the ban on hunting with dogs, according to a poll commissioned to coincide with the start of the hunting season this weekend.

The YouGov poll of more than 3,400 people, conducted last week, reveals that 59 per cent oppose the ban being overturned. And 63 per cent disagree that it amounts to an infringement of civil liberties. A large majority, 77 per cent, want to see the hunting ban properly enforced.

Opinion is divided on whether hunts are respecting the law – 32 per cent say hunts act within the law and 38 per cent believe they act illegally.

The poll, commissioned by the League Against Cruel Sports (Lacs), shows that one in seven (16 per cent) are in favour of prison sentences for people who break the law, with almost half, 48 per cent, in favour of people being fined up to £10,000.

Despite this being the first year of hunting under a pro-hunt Prime Minister since the ban came into force in 2004, there seems little prospect of one of the most controversial pieces of legislation passed by Labour being repealed. David Cameron has promised a "free vote on a motion" on a repeal of the Hunting Act, but campaigners claim any such vote would be lost.

Research by Lacs indicates that a minority of MPs – 253 out of 650 – are committed to repealing the Act. And 22 Conservative MPs are among more than 300 who would vote against a repeal.

Within Tory ranks, traditionally seen as pro-hunting, there is dissent. A pressure group, Conservativesagainstfoxhunting.com, was set up earlier this year. Its spokeswoman, Lorraine Platt, said: "We felt we were being misrepresented by the myth that all Conservatives were pro-hunting."

Douglas Batchelor, Lacs' chief executive, branded any hopes of reversing the ban a "pipe dream". He told The Independent on Sunday: "The hunts have realised that resistance is futile, public opposition to a repeal of the ban on hunting is sustained, and... we know there is no appetite in Parliament for repeal."

The Countryside Alliance dismissed the claims last night. A spokesman said: "We remain confident the case for repeal is absolutely clear; this is a useless and confusing, vindictive piece of legislation, and it is utterly wasting police time." Yet the alliance is keeping a low profile, its spokesman saying that it would be foolhardy to make hunting a priority when the economic situation was so dire.

Statistics released last Wednesday by the Ministry of Justice showed a surge in convictions under the Hunting Act, with 57 people convicted in 2009 – almost double the 33 in 2008. But the vast majority of offences committed under the Act have nothing to do with fox-hunting, claims the Countryside Alliance. "More people have been convicted of hunting rats than chasing foxes," the spokesman said. "There are 300 hunts across the country, each hunt twice or three times a week – that's something like one prosecution for every 32,500 hunting days."