There is also deep scepticism about the prime minister's motives about same-sex marriages, the Daily Mail reported.
Half of gays interviewed believe Cameron is doing it only to "make his party look more compassionate rather than because of his convictions".
The findings were from an online ComRes poll of 541 adults who described themselves as gay, lesbian or bisexual.
More than a quarter - 26 percent - believe there is no need to change the law on marriage because civil partnerships give couples the same rights.
And 72 percent believe marriage is "more about love between two people than it is about rearing children.
Austen Ivereigh, director of media advocacy group Catholic Voices, which commissioned the poll, said: "We asked ComRes to carry out this important survey because we knew many gay people were unhappy with the government's plan to redefine marriage."
"Gay people do not regard same-sex marriage as a priority, and show no more enthusiasm for it than for civil partnerships, which give the same legal advantages," he said.
Colin Hart of the Coalition for Marriage, said the poll confirmed that only a handful of people are pushing the government to redefine marriage.
"Even within the gay community, there is no majority who thinks that this is a priority," he said.
More than 543,000 people have signed a petition by the Coalition for Marriage which opposes any redefinition of marriage.
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