Gay rights supporters were urged to stamp out attempts by "a vocal minority" to block new legislation that seeks to legalise equal marriage in England and Wales.
The government published its Marriage (Same Sex Couples) Bill on Friday, but the legislation is likely to spark massive debate in the House of Commons where a significant number of Tory MPs oppose it.
Prime Minister David Cameron has given Conservative MPs a free vote on the Bill.
Stonewall is urging all supporters of equal marriage to contact MPs to back the Bill when they have their first chance to vote on the legislation in the House of Commons on February 5.
The gay rights charity pointed to an Ipsos Mori poll in December that found 73 per cent of people in Britain support equal marriage.
But the charity argued that most are not speaking out.
Stonewall chief executive Ben Summerskill said: "Sadly the minority of people who oppose equal marriage consistently use mistruths and smears to argue against it. Supporters of this modest measure mustn't let a vocal minority block equality.
"We need straight people with lesbian or gay friends or relatives to stand up for their rights too.
"Equality benefits everyone, which is why we need every supporter to press MPs to vote for it."
Shadow home secretary Yvette Cooper said: "Just as with civil partnerships in 2004 we look forward to passing this Bill into law with Labour votes."
Yet other campaigners say the legislation discriminates against straight couples who are still denied the right to a civil partnership.
Equal rights campaigner Peter Tatchell said: "Despite proclaiming that the legalisation of same-sex civil marriage is driven by the principle of equality, the government's forthcoming legislation will retain the inequality of the current legal ban on heterosexual civil partnerships.
"This will mean that for the first time in British law gay couples will have legal privileges over heterosexual couples.
"Some straight men and women don't like the patriarchal traditions of marriage.
"They'd prefer a civil partnership.
"Why shouldn't they have that option?"
Tory Culture Secretary Maria Miller said: "We feel that marriage is a good thing and we should be supporting more couples to marry and that is exactly what the proposals that were brought forward yesterday do."
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