The Conservatives' turmoil over David Cameron's plans for gay marriage has been compounded after Ukip pledged to exploit their divisions and go after the votes of Tories who abandon the party over the issue.

Amid signs that Conservative associations are losing members in their droves over what is being dubbed the prime minister's "clause IV moment", the Ukip leader, Nigel Farage, warned that gay marriage could "rip apart" the Conservative party. He plans to put the issue at the heart of Ukip's campaign for the 2014 European parliamentary elections.

The government set out its plans on Tuesday to introduce gay marriage by 2014. It also tried to appease more than 100 Tory MPs planning to vote against the legislation by outlining a new "quadruple lock" that will make it illegal for gay marriage ceremonies to be conducted by the Church of England and the Church in Wales.

Other religious organisations will be able to "opt in" to holding the ceremonies.

The law will also state that no one can be prosecuted for preaching the belief that marriage can be between a man and a woman only.

In a statement to MPs, the culture secretary and equalities minister, Maria Miller, said: "Because the churches of England and Wales have explicitly stated that they do not wish to conduct same-sex marriage, the legislation will explicitly state that it would be illegal for the churches of England and Wales to marry same-sex couples. That provision recognises and protects the unique and established nature of those churches."

The concession from Miller failed to win over the Church of England and many Tory MPs, including four ministerial aides and the former cabinet minister Cheryl Gillan, who stood up to denounce the plans. Andrew Selous, parliamentary private secretary to the work and pensions secretary, Iain Duncan Smith, said: "This legislation will mark a significant moment as this country will be passing a law that is directly contrary to what Jesus said about marriage in Mark chapter 10 and Matthew chapter 19."

A meeting between Miller and backbench MPs after her statement broke up abruptly when she arrived late after conducting a series of television interviews.

Peter Bone, the MP for Wellingborough, told Miller the government had no mandate for the change because it had not appeared in the coalition agreement or the Conservative or Liberal Democrat manifestos. He said: "You need a mandate for this. This whole exercise would have gone down well with Joseph Stalin."

One prominent Tory on the right voiced support, however. Bernard Jenkin said: "It is legislation not to change the society in which we live but to recognise how society has already changed … We should afford the freedom to marry to every citizen in this country."

Ukip made clear that it would exploit such Tory divisions in the runup to the European elections in June 2014, which will take place a few months after the legislation is due to come into force.

Farage told the Guardian: "David Cameron's proposal has the potential to rip apart the traditional rural Tory vote. While Ukip wholly respects the rights of gay people to have civil partnerships, we feel the prime minister's proposals will present an affront to millions of people in this country for whom this will be the final straw.

The division between city and rural is absolutely huge. In my village pub in Kent they are just completely against."

Farage believes the gay marriage issue will serve his party well by highlighting the impact of the European court of human rights on Britain and by showing Ukip can rally support around a touchstone issue. "Ukip is not a one-issue party," he said. "But the gay marriage case is closely interwoven with the European court of human rights, as is so much of our life. Ukip will be seen to be a party campaigning not just about who governs Britain but about how we think that Britain should be governed."

The intervention by Farage came as Tory associations confirmed that members have resigned over the issue. The Arundel and South Downs Association, whose MP, Nick Herbert, is a leading supporter of the plans, confirmed there had been resignations. Councillor Gordon Marples, deputy chairman of the association, said: "Views are polarised. We have seen people resign on a point of principle. It is contentious. It is a big issue. It is not something I would have sought. I don't have any particularly strong views on it. I just believe in equality and this is the way society is moving."

Marples said he would not fall out with Herbert, who faced Tory dissent when he told Miller in the Commons that opinion polls showed "widespread support for the change". Marples said: "I understand where Nick is coming from. He is in a civil partnership but he and I are not going to fall out on this. I understand David Cameron trying to modernise the Conservative party. But for most people it is rather like the AV vote – the timing seems to be quite unusual."

Councillor Frank Wilkinson, another officer of the Arundel association, offered strong personal support for Herbert, although he said he fundamentally disagreed with him. "If gay people want to have a civil ceremony that is fine by me, if they want to live together and love one another that is fine by me. But I am of the age now where I am a traditionalist – I have been married to my dear wife for 52 years – and I believe that marriage is between a man and a woman. I can't change my mind on that. But I have every respect for people who want to love their lives as they do."

Government whips claim that 60% of the Tory party's 303 MPs will support the proposals when MPs vote on the legislation next year. It will be passed only with the support of Labour and Lib Dem MPs.

Tory MPs will be given a free vote, allowing at least three cabinet ministers to vote against the change. Owen Paterson, the environment secretary, David Jones, the Wales secretary, and Philip Hammond, the defence secretary, have all voiced concerns. Duncan Smith does not agree with gay marriage, but he believes he needs to tread with care because, as a former Tory leader, he needs to show particular sensitivity.

The Church of England made clear that the concession from the government did not go far enough.

The Rev Tim Stephens, the Bishop of Leicester, said it was "most troubling that the government and opposition have together in their proceeding with this measure led to division, not only within the country where polls consistently show half the population against this change, but also between the political class and the vast majority of practicing religious people".

Archbishop Vincent Nichols, the leader of the Roman Catholic Church in England and Wales, and Archbishop Peter Smith, the Archbishop of Southwark, said opponents of gay marriage should lobby MPs "clearly, calmly and forcefully, and without impugning the motives of others". They said: "The meaning of marriage matters. It derives that meaning from its function as the foundation of the family."

The main group campaigning against the change – the Coalition for Marriage – is to try to win over more Tory MPs by warning that the issue could be what it is describing as Cameron's "Iraq moment". A source in the group said: "Tony Blair needed the support of Tory MPs to win the Iraq vote after 139 Labour MPs rebelled. It did lasting damage to his authority which he never recovered."

A new Ipsos-MORI poll for Freedom to Marry has found that three-quarters of voters support same-sex marriage. The most popular choice – 45% – was that gay people should be allowed to get married to each other but religious organisations should not be required to provide wedding ceremonies to gay people.

But a further 28% of voters thought that gay people should be allowed to get married to each other and religious organisations should be required to provide wedding ceremonies to gay people.

This means nearly three quarters of voters – 73% – want to allow gay marriage while less than a quarter – 24% – do not. Only one in six voters – 17% - thought that gay people should not be allowed to get married but should be allowed to form a civil partnership.

Ed Miliband moved to scotch rumours of divisions in the shadow cabinet. The Labour leader said: "The whole shadow cabinet is united in supporting same sex marriage together with the vast majority of all Labour MPs."

The gay rights campaigner Peter Tatchell condemned the exemption for the Church of England and the Church in Wales as "a disappointing fudge".

He said: "There is no reason why these churches should be treated differently from other faiths. The government is treating two churches differently from all other religions."

• This article was amended on 13 December 2012 to clarify that references in the original to "the churches of England and Wales" (which was the phrase used in the House of Commons by Maria Miller) were to the Church of England and the Church in Wales.