Affiliated gay groups in the Labour and Conservative parties have added their support to an amendment giving gay couples the right to religious civil partnerships.

An amendment to the Equality Bill will be tabled in the House of Lords tomorrow by out gay peer Lord Alli to give gay couples the new right.

Currently, civil partnerships legislation prohibits any religious elements to ceremonies but faiths such as Liberal Judaism, the Quakers and the Unitarians have said they wish to hold them.

Support is growing for the amendment and last week, faith leaders including the Bishop of Salisbury, the Dean of Southwark and five retired bishops wrote to The Times to argue that it was “inconsistent” and “discriminatory” to ban gay couples having their ceremonies in churches willing to accommodate them.

LGBT Labour co-chair Katie Hanson said: “Lord Alli has a strong and well-earned reputation for being at the forefront of the campaign for greater equality. As one of our patrons, we are proud to add our support to his amendment that would allow religious institutions the option of holding civil partnerships in their buildings.

“Many people wanting a civil partnership are people of faith too – and so where their religion consents, we believe it is right that they should be able to hold their ceremony in their place of worship.”

Matt Sephton, the Conservative candidate for Salford and Eccles, and the chairman of LGBTory, said: “There are many problems with the drafting of the Equalities Bill. However, Lord Alli’s amendment which allows civil partnerships to take place in religious buildings is a sentiment that I wholeheartedly support.

“In heterosexual marriage, there has always been a prohibition on civil ceremonies having a religious flavour as, presumably, if a couple want a religious marriage they can get married in a church or other place of worship. However, with civil partnerships, this is entirely different.

“It is therefore a completely logical step forward for places of worship to be able to host same-sex civil partnerships if they so wish. This would not be compulsory but an option for couples wanting to tie the knot and for religious institutions willing to accept and bless their commitment to each other as some religions and Christian denominations have indicated they would like to do.”