Gay and lesbian couples could soon win the right to marry, and straight couples be given the right to form civil partnerships.

The equalities minister, Lynne Featherstone, has disclosed that the government intends to consult over how marriage laws in England and Wales can be further reformed, despite strong opposition from some religious groups.

She confirmed the coalition's intention to go further, as the Home Office announced it is lifting the prohibition on civil partnership ceremonies being held in religious places of worship.

"Over the last few months I have spoken to a lot of lesbian, gay, bisexual and transgendered people and campaign groups and it became clear there is a real desire to address the differences between civil marriage and civil partnerships," said Featherstone. "We are going to be the first British government to formally look at what steps can be taken to address this."

The removal of the ban on civil partnerships in churches and other religious premises was agreed on a free vote in both houses of parliament in a late amendment to Labour's Equality Act 2010 before the coalition government came to power.

The home secretary, Theresa May, said the move would not be compulsory: "No religious group will be forced to host a civil partnership registration, but for those who wish to do so this is an important step forward." The change will affect England and Wales but not Scotland and Northern Ireland. A formal consultation paper will be issued in May.

The move was welcomed by the Quakers, Liberal Jews and Unitarians, but the Church of England and the Roman Catholic church were less than enthusiastic.

Michael Hutchinson for the Quakers said they were also heartened by proposals to address calls for full equality of civil marriages and civil partnerships: "Our religious experience teaches us to seek a change in the law so that same-sex marriages can be celebrated, witnessed and reported to the state in the same way as heterosexual marriages."

Human rights campaigner Peter Tatchell said the proposals were "a significant advance for gay and religious freedom".

"It was petty and authoritarian to ban faith organisations like the Quakers from holding civil partnership ceremonies, when they clearly expressed a wish to do so," he said. "The old restrictions forced religious bodies to discriminate against same-sex couples, even when they didn't want to." The government's failure to open up marriage for LGBT people was "spineless", he said.

But the Church of England said the House of Bishops had taken a consistent view that vicars should not provide services of blessing for those who register civil partnerships. A spokesperson said it could lead to inconsistencies with civil marriage and to confusion for churches and faiths.

Conservative evangelical groups such as Affinity and the Christian Institute demanded protection against legal action for refusing to host civil partnerships.

But the Rev Stephen Coles, a gay vicar from St Thomas's, Finsbury Park, north London, said it would encourage denominations reluctant to hold such ceremonies to think again: "Those who are at the moment finding all this very difficult, it just might mean that they become more stubborn.

"I also think the number in the church who are opposed is smaller than people think – but they are very noisy."

Eight British couples filed a joint legal application to the European court of human rights last week seeking to overturn the twin bans on gay civil marriages and heterosexual civil partnerships.