The vehemence of Conservative divisions over same-sex marriage were exposed when one Tory MP said it would undermine "normal marriage", another questioned whether polygamy would be legalised next, and a third claimed that European judges will soon force the Church of England to allow same-sex marriages against its will.

A fourth Tory MP David Davies, the MP for Monmouth and chair of the Welsh Affairs Select Committee insisted he was not a bigot because as a boxer he had once trained with a gay boxer. He tweeted: "Once fought gay boxer. Respect & like. trained with after bout so not bigoted. activists calm down – listen to other views."

He had earlier said he did not believe most parents wanted to have gay children because they wanted to be grandparents. The Tory tensions emerged as Maria Miller, the culture secretary, told MPs she would be publishing detailed plans to allow same-sex marriage on Tuesday. She infuriated some of her party's backbenchers by saying the reform was not about style, modernity or fashion, but about fairness and equality.

Ministers have already confirmed they will allow religious organisations to opt in to allow same-sex marriages, a move the government believes will increase protection for churches opposed to same-sex marriage from legal challenges under the European convention on human rights.

A small number of churches – the Unitarians, Quakers, and Jewish liberals – would like to administer same-sex marriages. The consultation will also make it clear that if the General Synod of the Church of England continues to oppose same-sex marriage, individual dioceses will not be free to offer marriages to gay or lesbian couples.

Miller told MPs that the government had received legal advice that there was a "negligible" risk of a legal challenge to the legislation through either British or European courts. She said there were "clear protections" for religious institutions and "the rulings in European case law have made clear that these issues are for individual countries and not something they will rule on centrally".

She said many churches had not faced legal challenges even though they apply different rules on issues such as the remarriage of divorcees, or will only allow marriages of their own fellowships.

Miller added that the rights of teachers to espouse a Christian view of marriage would not be altered by her proposals. She claimed there had been a great deal of hyperbole and scaremongering about her plans, a reference to the literature put out by the Coalition for Marriage.

Many Tory MPs expressed fears that human rights legal challenges will sweep aside the protections promised by Miller. Robert Haflon, the MP for Harlow, pointed to the threatened imposition of votes for prisoners by the European court of human rights.

Dr Matthew Offord, MP for Hendon, asked if the government was going to introduce other forms of marriage, such as polygamy. Bob Stewart, the MP for Beckenham, accused the government of "being hellbent on upsetting so many thousands of our citizens in normal marriages".

Gordon Henderson, the MP for Sittingbourne, said it was "a fact and not scaremongering" that redefining marriage in the way planned would have an impact on religous beliefs.

Many Tory MPs admit they have been under intense pressure from vociferous lobbies in their constituencies, with 250,000 responses to the government consultation. The Coalition for Marriage claims as many as 100 Tory MPs will take advantage of the free vote and oppose same-sex marriage.

Cameron, determined to show his party has irreversibly modernised, said of the reform: "I believe it will be passed and passed with a big majority because I think the time for this has come." He has tried to draw the poison from the divisions in the party by giving his MPs a free vote when a bill is brought to the Commons sometime before Easter.

Labour will face its own problems if Ed Miliband goes ahead with plans to whip his MPs on the issue, a move that might present difficulties for Stephen Timms, the shadow employment minister and an evangelical Christian.Miliband has been advised to allow a free vote to avoid distracting from the serious divisions among the Tories. A free vote on the Labour side would not prevent supporters of same-sex marriage winning a Commons vote since the number of Labour MPs opposed to the measure is probably fewer than 10.

Miller was forced by the Speaker to make a preliminary statement on the issue after Cameron on Friday said he would support same-sex marriage.

Edward Leigh, the Conservative MP for Gainsborough, accused the prime minister of changing the terms of the consultation by saying he now wanted to legislate for same-sex marriages in churches, something the consultation specifically excluded by focusing solely on civil marriages. He said the change in policy greatly increased the chance of human rights litigation to force churches against their will to have same-sex marriages.

Nick Herbert, the former Home Office minister, said that while civil partnerships were an incredibly important step forward for gay people, "those civil partnerships are not marriages, and gay people will not feel they are fully accepted in society while they are denied access to one of our most important institutions".

Peter Bottomley, another supporter of reform, accused the Coaliton for Marriage of disgusting behaviour saying it had sent out hundreds of thousands of letters trying to persaude MPs that they would lose their support if they supported gay marriage.