The ComRes poll found that 54% of people want a public vote on the controversial plans, which did not feature in any of the parties' manifestos. Just 26% disagreed.
There was also strong support for the existing definition of marriage to be retained.
Asked if marriage should continue to mean the lifelong commitment between a man and a woman, 62 per cent agreed compared to just 28 per cent who disagreed.
Among Conservative voters this figure rose to 68 per cent.
The poll also suggested that the Prime Minister's marriage plans are going to cost the Tories votes at the next General Election.
By a majority of 8:1, those who voted Conservative in 2010 but say they no longer intend to, revealed that gay marriage had put them off returning to the Tory fold.
The hardening attitude could mean a loss of up to 1.35 million votes - or around 13% of those who voted for the Tories in the last election.
There is also strong suspicion surrounding the Prime Minister's motives, with nearly seven in 10 people (65%) agreeing that the policy was being pushed to make the Tory party look trendy and modern, and not because of Cameron's personal convictions.
Colin Hart, campaign director of the Coalition for Marriage said: “This latest poll confirms that it is unpopular with all voters, but particularly Conservatives, who want a referendum on the issue. They want this, because these ordinary men and women have never been able to cast a vote on the issue as neither the Conservatives, Lib Dems, or Labour included this proposal in their manifestos and they are fed up with being told it is going to happen regardless of what the majority of people in this country believe.”