Labour has accused the government of making a "real mess" of its equal-marriage proposals and urged a rethink after the Church of England and the Church in Wales said they were not consulted over plans to ban them from offering same-sex ceremonies.

Yvette Cooper, the shadow home secretary and minister for women and equality, intervened as the archbishop of Wales complained that the government had put his church in an "enormously difficult position", which threatened to "severely curtail" its freedom to act according to its conscience.

The churches said on Thursday they had no idea they were to be legally barred from marrying same-sex couples until the culture secretary and equalities minister, Maria Miller, outlined the proposals to the Commons on Tuesday.

"Ministers have made a real mess of this," said Cooper. "Why are they making it expressly illegal for the Church of England and the Church in Wales to hold same sex marriages, when even senior figures in both churches are questioning it?

"The government should rethink this before they publish the legislation. Religious freedom should be protected in the legislation. But that goes both ways. Churches that want to hold same-sex marriages should be able to do so."

Cooper, who said Labour would consider amending the bill once it was published if the government did not start listening, also asked the Church of England to reconsider its opposition to the matter.

"Although the Church of England has said it does not support same-sex marriage right now I hope it will change its position in time," she said. "Parliament should not be making it harder for any church to change its mind in future – especially the established church."

The archbishop of Wales, Dr Barry Morgan, said he felt the wishes of the Church in Wales had not been heeded by the government.

"We didn't even have informal contacts with officials," he told BBC Radio 4's World at One. "The Church of England may have had that, but the Church in Wales certainly did not. I think we were just regarded as a kind of tag-on, as it were.

"It has put us in an enormously difficult position … It would have been nice to have some kind of consultation with somebody."

The archbishop said the church was speaking now to Miller and other officials in the hope of changing the government's mind.

"To regard the marriage of gays as a criminal act I don't think helps anybody," he said. "It certainly doesn't help the church and it doesn't help gay people either.

"It's not law yet and there is a long way to go, so I'm hoping we will be able to find a way round it that doesn't lock us in this protection."

A government spokeswoman said it was "just not true" to say that it had failed to discuss its proposals with the Church of England, and denied the church's assertion that it had not been informed of the so-called "quadruple lock" on gay marriage.

She said: "While it is inappropriate to share the exact nature of legislative proposals before announcing them to parliament, discussions with the church were quite specific about the quad lock."

The church, meanwhile, stressed the need for consultation saying it had "underlined to the DCMS the importance of church officials being able to study draft clauses before the bill is published, given the complex interaction between statute law and canon law".

A spokeswoman for the Catholic church in England and Wales said the church had nothing to add to the statement it made on Tuesday, in which it described the process behind the proposals as "shambolic".

The government proposals, which come after last month's General Synod vote against legislation to allow female bishops, have disheartened many clergy campaigning for a more inclusive church.

Colin Coward, director of Changing Attitude, which works for the full inclusion of gay, lesbian, bisexual and transgender people in the life of the Anglican Communion, said he felt the row had reinforced the perception that the church was homophobic and made life far more difficult for the next archbishop of Canterbury, Justin Welby.

"I think he could have coped with the mess that had been created in the aftermath of General Synod," he said. "I think the mess that is now being created is much more difficult for even somebody as wise and skilled as him to deal with. It's easy to look at what's happening and see the church entering more and more deeply into a crisis from which it may not manage to clamber out."

Father Andrew Cain, vicar of St Mary with All Souls, Kilburn and St James, West Hampstead, and a campaigner for equality and inclusion within the church, said the struggle for equal marriage was reminiscent of the fight for women priests.

"Twenty years ago, we had no women priests; we're now debating women bishops," he said. "The whole campaign for equal treatment of gays and lesbians in the church is 20 or 30 years behind that of women. We just have to keep campaigning and eventually, the church will catch up with society - hopefully slightly faster."

The Rev Bob Callaghan, national co-ordinator of Inclusive Church, said he was not holding his breath.

"It ain't going to happen in my lifetime as a priest," he said. "I'm 53 and I ain't going to be doing gay marriages. Come off it. We'll be lucky to have women bishops by the time I'm still ministering. But I think there is a need to keep plugging away at it."