Image caption An estimated 300 hunts are held on Boxing Day

The Conservatives do not have the parliamentary majority to overturn a ban on hunting with dogs in England and Wales, the Tory Party chairman said.

Grant Shapps said he agreed with Environment Secretary Owen Paterson that a free vote for MPs on lifting the ban would be defeated.

Mr Paterson earlier said that a vote may not happen in 2013.

It has been illegal to use dogs to hunt animals in England and Wales since 2005, and in Scotland since 2002.

Mr Shapps, speaking on BBC Radio 4's The World At One programme, said: "As Owen Patterson said, it makes sense to bring something forward if you think there's a chance of there being a Parliamentary majority.

"At the moment there doesn't appear to be one."

More than 300 hunts are holding Boxing Day meets, a week after the RSPCA's first successful prosecution of a hunt for operating illegally.

Analysis Environment Secretary Owen Paterson is seen by those on the right of the Conservative Party as an authentic Tory who shares their instincts. But Mr Paterson's comments show he is a mathematically astute pragmatist. Yes, the coalition agreement sets out the government will give MPs a free vote on repealing the Hunting Act. But the environment secretary has done his sums and concluded those in favour of overturning the law would lose. Some Conservatives will also be very aware that reintroducing the debate on hunting at Westminster would open a whacking great dividing line with Labour. Ed Miliband's party would argue pushing for a vote would prove the Tories are out of touch with the concerns of most voters. How long will France hunt with hounds?

Hunts are no longer allowed to use dogs to chase foxes, but are instead supposed to use techniques such as drag hunting, where dogs set off on the trail of a scent laid about 20 minutes in advance by a runner or rider dragging a lure.

Mr Paterson told the Daily Telegraph: "At the moment, it would not be my proposal to bring forward a vote we were going to lose."

A free vote on the issue is included in the coalition agreement, although Mr Shapps said: "Hunting hasn't been a feature of this Parliament."

Tory backbencher Simon Hart, a former chief executive of the Countryside Alliance, said he believed Prime Minister David Cameron still intended to honour the commitment to hold a free vote.

"He knows that he has made a promise on this, he knows he can't really afford to let down core voters in rural constituencies and nothing he has said in the last two-and-a-half years to me has indicated that he has slipped an inch on this," he told the BBC.

A spokesperson for the Department for Environment, Food and Rural Affairs confirmed: "The coalition government pledged to put forward a motion to allow a free vote on the Hunting Act.

"This will take place at an appropriate time and if parliament were to vote in favour of repeal, the government would introduce a Repeal Bill in the House of Parliament in due course."

Responding to Mr Paterson's comments, the shadow environment secretary, Mary Creagh, said "most people back Labour's ban on hunting wild animals with dogs".

Animal welfare charities, including the RSPCA and the League Against Cruel Sports (LACS), have commissioned research which suggests that only 15% of people want to scrap the ban.

But the Countryside Alliance says it has seen no slackening of support for hunting in recent years.