A new campaign against same-sex couples marrying, Keep Marriage Special, has claimed in glossy leaflets that the next logical step will be legalising incest and polygamy. Out4Marriage has branded the group’s claims “extremist and confused”.

The new lobby group formed by MPs and bishops adds to the campaign against equality currently led by the Coalition for Marriage.

An eight-page glossy leaflet featuring a mixed-race heterosexual couple on the cover warns of the “consequential impact” of David Cameron’s pledge to introduce equal civil marriage for same-sex couples.

The document claims that “if the only basis for marriage is the desire of the parties to get married then there is, according to the logic of this proposal, no reason not to open up marriage to more than just same-sex couples. Polygamy, polyandry and incest would all be permissible.”

It also says that “the immigration service is already swamped with false marriages – this would only add to their problems.”

It claims that its stance against allowing gay couples to marry are not homophobic in nature. “There is nothing homophobic about stating the biblical position that all sexual activity outside marriage is wrong,” the leaflet claims. “Christians must show love to all people and are themselves sinners whose sins have been forgiven. They have a duty to tell the truth about right and wrong and to proclaim the good news that God forgives the sins of all who repent and trust in Jesus Christ.”

The new group is backed by the former bishop of Rochester, the Rt Rev Michael Nazir Ali and Bishop David Samuel, president of the Protestant Reformation Society. It also claims the backing of two Democratic Unionist MPs Nigel Dodds and Jeffrey Donaldson, although they represent Northern Irish constituencies, where there are no proposals to introduce equal marriage. David Cameron is proposing equal civil marriage for England and Wales, the Scottish Government is going through its own process while the Government in Northern Ireland is not proposing to introduce equal marriage.

Meanwhile, Out4Marriage, the online campaign for equal marriage launched by PinkNews.co.uk founder Benjamin Cohen has drawn support from Deputy Prime Minister Nick Clegg,  Home Secretary Theresa MayShadow Chancellor Ed BallsShadow Home Secretary Yvonne CooperSir Richard Branson, the Virgin founder; The Saturdays girl groupJack Straw, the former Foreign Secretary; David Walliams, the  Britain’s Got Talent judge; Caroline Lucas, the leader of the Green party; Lynne Featherstone, the Lib Dem Equalities Minister; Peter Tatchell, the  gay rights campaigner; and Lord (Chris) Smith), the Advertising Standards Authority chairman among many others.

Ethan Bourne, a spokesman for Out4Marriage branded Keep Marriage Special’s claims “extremist and confused”. He said: “Neither the LGBT community or the Government are calling or proposing to legalise incest or polygamy, but instead to allow marriage between two people of the same sex who love each other and that the law already says can be in a relationship with one another. The Keep Marriage Special campaign is talking about a different issue altogether, deliberately constructed to provoke fear and revulsion.”

In his video for Out4Marriage, Deputy Prime Minister Nick Clegg said: “All couples should be able to make that commitment to one another, regardless of who they love.

“I fought for equal marriage before I was in Government, and I’m even more committed to making it happen now – as a Liberal Democrat and as Deputy Prime Minister.

“We brought forward our proposals – they have provoked a heated debate.

“But these are proposals about when and how to open up civil marriage to gay and lesbian couples. It’s not a matter of ‘if’ any more.

“And to those who are worried about some of the opposition to this move or the tone of the debate, let me just say, whether you are a gay, lesbian, bisexual, transsexual or straight: your freedom to love who you choose is a fundamental right in a liberal society – and you will always have our support. That’s why I’m Out4Marriage.”