Nick Clegg has criticised David Cameron for allowing Conservative MPs a free vote on government measures to legalise gay marriage. The Liberal Democrat deputy prime minister said on Sunday that it was wrong to describe this as a matter of conscience and he did not want the parliamentary vote on this to become "a great free-for-all".

Several Tory MPs are strongly opposed to allowing gay marriage. On Thursday Sir George Young, the Conservative leader of the Commons, announced that there would be a free vote on the subject because it was a matter of conscience.

The matter is was depicted as a U-turn because Downing Street had previously said that collective cabinet responsibility would apply to the decision. But this stance was undermined when it emerged that Owen Paterson, the Northern Ireland secretary, had told a constituent he would not support gay marriage. Speaking on BBC1's Andrew Marr show, Clegg said he did not accept that this was a matter of conscience. "If this was an issue that somehow the government was proposing, something which would be an imposition on religion or the churches then, of course, that would be a matter of conscience. We are not," he said.

Clegg argued that when the last Labour government introduced legislation to allow same-sex couples to enter into civil partnerships – that came into force in December 2005 – the commons vote was whipped. "I personally don't think this is something that should be subject to a great free-for-all because we're not asking people to make a decision of conscience about religion," he went on.

Cameron announced his support for gay marriage at the Conservative party conference in 2011. But the polls suggest that more Tory supporters are opposed to gay marriages than in favour.

After the party received a drubbing in the local elections, many councillors and MPs claimed that gay marriage – and particularly the impression that Cameron was making this a priority – was in large part to blame.

Since then, Cameron has been playing down its importance as an issue. There was no mention of gay marriage in the Queen's speech, and the legislation could be delayed for some years.

Cameron's decision to allow a free vote increases the chances of the legislation being blocked when MPs eventually do vote on it, although there is no evidence yet to suggest that the opponents of gay marriage have enough support in parliament to block the measure.