Campaigners are seeking to get an amendment tabled to the Equality Bill to allow religious buildings to hold civil partnership ceremonies.
The amendment would give ministers of religion the option of presiding over the ceremonies and would not be compulsory, reports Pink News.
When civil partnerships came into law, a prohibition was placed on their being held in religious buildings. They must instead be carried out in other buildings licenced to host them.
Many churches also oppose holding civil partnerships but some denominations such as the Quakers have expressed their support for recognising gay couples. This year, the Quakers agreed to hold same-sex marriages, rather than civil partnerships.
Stonewall is working with the Lesbian and Gay Christian Movement (LGCM) and the Metropolitan Community Church to get the amendment tabled. This is likely to happen when the bill is moved before the House of Lords in the next four to six weeks.
Rev Sharon Ferguson, of the LGCM, told PinkNews.co.uk: "As far as I know, civil partnerships are really good in that they give us legal protection. But they do not give equality. Lesbian and gay people can only have a civil ceremony but heterosexual people have the choice.
"I'm not bothered about calling civil partnerships marriage – that's just semantics. I want to see equality in that any body registered and licenced to conduct a marriage can also conduct a civil partnership. And any building registered to conduct a marriage can also conduct a civil partnership.
"For those ministers of religion who are happy to conduct a civil partnership, they should be able to do so. It doesn't have to be compulsory. All ministers of religion have the right to refuse any heterosexual couple marriage."
Rev Ferguson added: "It's no major change, no major political work. But the objection will obviously come from the House of Lords, where there are lots of bishops, and the religious right."
She added that she wanted to see civil partnerships also available to straight couples.