Delegates at the party's annual conference in Liverpool support call for marriage equality for lesbian, gay, bisexual and transgendered people

Liberal Democrats today overwhelmingly backed moves to allow same-sex and mixed-sex couples to choose whether they wish to have a marriage or a civil partnership and to allow gay couples to have a church wedding.

Evan Harris, the former MP for Oxford West and Abingdon, said the motion would "test" the Conservatives' commitment to equality and would strengthen the hand of Lib Dem equalities minister, Lynne Featherstone, in pressing for a change in the law.

Harris told delegates at the party's annual conference in Liverpool that the party should use the fact that it was part of the coalition government to "seize the moment to push the agenda forward on full equality".

Harris challenged the belief that equality for lesbian, gay, bisexual and transgendered people (LGBT) had been achieved under the Labour government following a raft of legislation over the past 13 years, including lowering the age of consent and introducing civil partnerships for same-sex couples.

Section 28, the legislation introduced under the Conservatives that banned the "promotion of homosexuality" by local authorities, took many years to repeal, he said, and Labour also held back from outlawing gay discrimination in the armed forces until a court ruling overturned the decision.

Hailing the Lib Dems' record on equality issues, Harris said: "We have never failed to do that in the past. There's plenty of work still to do. Let's give Lynne and other Liberal Democrats in government something to get their teeth into."

A change in the law would ensure transgender people would not be forced to divorce their wife or husband before they could achieve a gender change, he went on.

Aware of the sensitivities of religious groups, he insisted the motion would not force religious groups to conduct ceremonies if they did not wish to do so.

Liz Williams, a Lib Dem from the Leyton and Wanstead branch and a member of the party's Christian fellowship, told delegates that she has supported same-sex marriage for 20 years because her "Anglo-Catholic faith" taught her that marriage was a sacrament and an outward, physical sign of an inward and spiritual grace.

Williams said: "The grace of marriage is the love that unites people. I cannot deny and do not want to deny in the lives my gay, lesbian, transgendered and bisexual friends, the same love and grace that I espouse and display in my own."

The motion calls on the government to open both marriage and civil partnerships to both same-sex and mixed-sex couples and also allow approved religious and humanist groups to celebrate marriage or civil partnerships in "any authorised place".

People who change their gender would be allowed to remain in a current marriage or civil partnership under the plan.

The motion also calls for a straightforward change to allow civil partnerships to be converted into marriages.

Gay couples married outside the UK would have their relationship automatically recognised in the UK.

This change would apply to Brian Paddick, a retired senior police chief who stood as the Lib Dems' mayoral candidate in 2008, and told the conference he married his partner in Oslo in an "intensely moving" ceremony.

He told the conference: "We are married. It is important. Yet we are only married in Norway. Here it reverts to a civil partnership and that doesn't feel the same at all.

"Yes, we have to be sensitive to religions and what they feel on this issue, and we are not talking necessarily about forcing religions to marry same-sex people in their synagogues and churches and temples.

"But what we are saying is that there should be equality. If I want to marry my same-sex partner then I should be allowed to do that."

Liberal Democrat MP Stephen Gilbert rounded on Stonewall, the prominent lesbian and gay charity, whose chief executive, Ben Summerskill, told a fringe meeting last night that it opposed the motion.

"You've done so much for the gay community, but on this, you've got it wrong," said Gilbert. "It should not be up to me as a member of parliament to lobby Stonewall on equal rights. It should be Stonewall lobbying me."

Summerskill said the claim was "categorically not true", since the organisation had yet to declare its position on gay marriages as the next step to civil partnerships.

Summerskill told the Guardian: "We have declined to express a view on this. The reason is that we are consulting our 20,000 supporters and once we have built a consensus on this issue we will make it clear."

Gilbert acknowledged the motion was controversial, telling the conference: "Of course, there will be opponents. When it comes to equality, you and I all know that there are opponents. But let's be clear. This motion doesn't compel religious groups to offer gay marriage or compel gay people to get married. It simply extends an equal choice to one and all."