Quakers in Britain, Unitarians and Liberal Judaism have written to the Prime Minister urging him to see through his commitment to change marriage laws to enable gay couples to marry and asking him to allow them to perform gay weddings.

The groups have written an open letter to Prime Minister David Cameron as the government’s public consultation on how to implement civil marriage equality for gay and straight couples enters its final weeks.

The government does not currently propose to allow religious bodies to hold weddings for gay couples, a ban the three denominations would like to see lifted.

The joint letter says: “We welcome your commitment to change marriage laws to enable same-sex partners to marry and offer you our prayerful support at this time. We know that you are hearing strong views about this from all around you.

“Quakers in Britain, Unitarians and Liberal Judaism are all committed to equality of marriage and ask that any legislation will mean we are free to conduct same-sex marriages in our places of worship.

“This is about religious liberty for us, so we don’t expect parliament to force others, who may disagree with us, to marry same-sex couples if they do not wish.

“We urge you to stand firm and show moral leadership on this issue, which affects the lives of many real people in this country. If, as you have said, same-sex marriage is the right thing to do, then it’s right to do it properly, and it’s right to do it now.

“We would welcome your assurance that this issue remains a priority of the coalition government.”

Quaker Recording Clerk, Paul Parker said: “Fifty years’ careful thinking led Quakers in 2009 to work for a change in the law to allow equal marriage and so we welcome the prime minister’s personal commitment to allow this. However, we are concerned the tone of the debate is changing, even before the Consultation is complete.” There has been talk of Tories having a free vote on the plan to allow same-sex couples in England and Wales to marry and one cabinet minister has said he will not vote for it.

The letter was signed by Derek McAuley, Chief Officer of Unitarian and Free Christian Churches; Paul Parker, Recording Clerk for Quakers in Britain; and Danny Rich, Chief Executive for Liberal Judaism.