David Cameron is facing a backlash from traditional Conservatives after he confirmed plans to allow churches and religious organisations to host same-sex weddings.

Opponents of gay marriage claim more than 120 Tory backbenchers will reject the plans in the free vote promised in the Commons. Details of the draft legislation will be unveiled next week.

The prime minister is backing the proposal in the face of opposition from the Church of England and the Catholic hierarchy. He supports a compromise through what is known as a permissive clause that allows gay marriages to be held in places of worship but does not oblige religious organisations to hold same-sex weddings.

Speaking in Redditch, Cameron said: "I'm a massive supporter of marriage and I don't want gay people to be excluded from a great institution. But let me be absolutely 100% clear, if there is any church or any synagogue or any mosque that doesn't want to have a gay marriage it will not, absolutely must not, be forced to hold it.

"That is absolutely clear in the legislation. Also let me make clear, this is a free vote for members of parliament, but personally I will be supporting it."

One cabinet minister has said he will vote against the proposals and believes at least three others will also refuse their support. "This is a sad day. I don't want to oppose the PM's wishes, but I haven't much choice," he said.

David Burrowes, Conservative MP for Enfield Southgate and parliamentary private secretary to the environment secretary, Owen Paterson, told the Guardian there are several members of the cabinet who will vote against or abstain.

"I have spoken to many Conservative MPs about this and a majority are against this particular change," he said. "These proposals raise many more questions than they answer. The so-called protections will not be sufficient.

"It is an attempt by the state to redefine marriage. This is not just about the freedom of churches to administer gay weddings. It is about the freedom of public sector workers and others to exercise their liberty of conscience. It has opened a can of worms," he said.

Despite the rebellion, the proposals should get through the Commons because most Liberal and Labour MPs are expected to back them. There may be a bigger fight in the Lords.

The deputy prime minister, Nick Clegg, also voiced his support. "I'm a supporter and always have been of same sex marriage, because I think marriage is a wonderful thing, a wonderful institution," he said during a visit to the south-west. "It's a demonstration of a couple's commitment to each other, of their loving relationship and they wish to celebrate that in the eyes of society and I think we should make that celebration, that ceremony if you like, available to everyone regardless of who they are.

"It's very important to remember that in our plans we're not going to force any church or any religious denomination to hold same sex marriage ceremonies if they don't want to but I do think it's time that we allow any couple, no matter who they are, to marry if that's what they want to do."

Under the proposals, governing bodies of each faith will be able to opt-in or opt-out of holding gay marriages; individual parishes will not be able to adopt different positions.

A government spokesman added: "We are committed to bringing equal civil marriage forward and the consultation results will be announced next week. We are very clear that religious organisations must be protected and that none will be forced to conduct same-sex marriage.

"EU law is very clear that this is the case and we will additionally bring in very strong legal locks to ensure that this is watertight."

Although the UK's main churches oppose the reform, other groups, including the Quakers, Unitarians and liberal Judaism, support marriage rights for gay couples and have said they would like to conduct the ceremonies.

Benjamin Cohen, of Out4Marriage, which campaigns for same-sex weddings, said: "We're delighted to hear that the government will be legislating to introduce full equal marriage including same-sex marriages solemnised by religious ministers.

"Legislation must give individual religious organisations the freedom to decide for themselves whether to hold same-sex marriages. None should be forced to, but those that wish to must be given the rights to do so."

Paul Parker, recording clerk for Quakers in Britain, said: "Quakers have been discussing sexuality for 50 years and in 2009 that led us to seek a change in the law so that all marriages in Quaker meeting houses, of whatever sex, can be prepared, celebrated, witnessed, reported to the state, and recognised as legally valid, without further process.

"We are waiting for the law to catch up. For Quakers, this is an issue of religious freedom and we don't seek to impose this on others."

Meanwhile, the gay rights campaigner Peter Tatchell said that under the new law, heterosexual couples would have fewer rights than gay couples.

He said: "Despite proclaiming that the legalisation of same-sex civil marriage is driven by the principle of equality, David Cameron is expected to retain the inequality of the current legal ban on heterosexual civil partnerships.

"Opposite-sex couples are legally prohibited from having a civil partnership and David Cameron intends to keep it that way. This will mean gay couples will soon have legal privileges over heterosexual couples.

"There will be two forms of official state recognition for lesbian and gay couples: the present system of civil partnerships and the new system of civil marriages. Heterosexual couples will have only one option: marriage. They will be subjected to legal inequality and discrimination. This is very wrong. I support straight equality."

Ayesha Vardag, a divorce lawyer, comments: "Civil partnership is almost identical in law to marriage, and is treated by the Courts in the same way … However setting up a distinction, albeit in name only, has caused confusion in the public generally and resentment among gay couples who feel they are being put on a sort of 'second tier' civil partnership track subordinate to their married heterosexual counterparts. We now have heterosexual couples saying they like the look of civil partnership for themselves and gay couple wanting marriage, when in reality they are the same thing."

Andrea Minichiello Williams, director of the Christian Legal Centre, said: "We have seen countless cases where Christians have been forced out of their jobs for their refusal to condone and promote homosexual practice. Their views have not been respected or accommodated and Mr Cameron has ignored their plight.

"This does not bode well for British Christians if further legislation is passed. Assurances to churches who do not wish to perform same-sex 'marriages' fly in the face of all the evidence."

Jonathan West, head of Family and Matrimonial law at city law firm Prolegal said: "The prime minister's desire to give religious institutions the chance to offer marriage services for same-sex couples is welcome, but it doesn't go far enough.

Religious institutions currently exist in a legal niche where they can discriminate on the basis of sexuality against same-sex couples. However, Governments should not shy away from attacking discriminatory practices in every part of society. Apart from religious bodies, any institution which engages in this form of discrimination would be pilloried by public opinion and would certainly be on the wrong side of the law."