James-J Walsh, campaigns director for Out4Marriage, said it was more important than ever that Holyrood passed its own proposals after the Marriage (Same Sex Couples) Bill successfully cleared the House of Lords.
The proposals are on course to become law within days. Mr Walsh described the move as "a momentous occasion in lesbian and gay equality in England and Wales, overcoming the last major hurdle on our path to full legislative equality".
He added: "Our work is not yet complete, we must now ensure that Scotland, Northern Ireland, the rest of the Commonwealth and world comes Out4Marriage."
Dozens of supporters wore pink carnations in the Lords to see the Bill receive an unopposed third reading, openly gay Labour peer Lord Alli thanked peers in an emotional speech, declaring: "My life and many others will be better today than it was yesterday."
Deputy Prime Minister Nick Clegg told campaigners outside that the new law would ensure that lesbian, gay, bisexual and transgender people felt "recognised and valued, not excluded".
However, opponents of gay marriage warned that the controversial Government-backed reform would return to bite Prime Minister David Cameron. The Coalition for Marriage campaign group said it would mobilise a 700,000-strong support base in next year's European elections and the general election of 2015.
The Bill survived a stormy passage through the Commons despite fierce opposition from dozens of Tory backbenchers, and then overcame an attempt to "wreck" it in the House of Lords last month.
Government women and equalities spokeswoman Baroness Stowell of Beeston hailed the legislation as a "force for good". But Tory Lord Framlingham complained it had been "bulldozed" through Parliament and said: "Happiness won at the expense of other people's happiness is rarely trouble-free in the long term."
Stonewall chief executive Ben Summerskill said: 'It's impossible to express how much joy this historic step will bring to tens of thousands of gay people and their families and friends."
Equal Love campaign co-ordinator Peter Tatchell said it was a vote that defeated discrimination and a victory for love and marriage after 21 years of campaigning.
Paul Parker, recording clerk for Quakers, which plans to stage the nuptials, said it "brings us tantalisingly close to legal recognition for same-sex marriages in our Quaker meetings".
The Scottish Government published its gay marriage Bill at Holyrood last month as part of a deal with Westminster to amend the UK Equality Act.