More voters want David Cameron to dump his plans to redefine marriage than want him to drop the policy of plain packaging for tobacco.
A poll by ComRes for the Coalition for Marriage asked 2,000 adults which of the two policies they would prefer to be abandoned.
Over a third (34 per cent) wanted Mr Cameron to dump redefining marriage, while only 28 per cent favoured ending proposals for plain packaging for tobacco.
Among those who voted Conservative at the last general election, 46 per cent wanted same-sex marriage legislation dropped.
Only 22 per cent of those who voted Tory in 2010 would rather see the tobacco plans abandoned.
The Government has already indicted it will back away from plans about tobacco packaging, but it will continue with the redefinition of marriage.
Colin Hart, campaign director for the Coalition for Marriage, said: “This poll yet again shows how out of touch David Cameron is with his own party and the public at large.
“The Prime Minister still remains determined to force through this undemocratic and unpopular legislation, which has never been voted upon by the electorate and which contributed to the disastrous local election results.
“Poll after poll has found that this issue could cost the Conservatives more than a million votes and the next general election.”