In contrast, research by PinkNews.co.uk, involving an 864-strong panel, shows that the backing of gay voters for Nick Clegg's Liberal Democrats mirrors society as a whole and has slumped by one-third.
The findings come as Lynne Featherstone, the LibDem international development minister, hit back at church leaders, saying their arguments in opposition to gay marriage are shameful, while Tory Nick Herbert, the former police minister, said he was troubled by the tone of interventions by Catholic leaders.
The poll shows support among gay, lesbian, bisexual and transgender (LGBT) voters for the Tories has risen from 11% at the 2010 General Election to 30%. Two-thirds of those surveyed said the Conservatives' backing for gay marriage had made them look at the party in a more positive light.
In 2010, the LibDems were easily the most popular choice for LGBT voters with 39% support but this has now plummeted to just 13%.
Labour, meanwhile, now attracts 38% of the LGBT vote compared with 27% at the last General Election.
Benjamin Cohen, the PinkNews publisher, said: "By proposing same-sex marriage, David Cameron has unquestionably improved the standing of the Conservative Party among the gay community.
"However, what's most interesting is that he is considerably more popular than his party within our community."