The Church of England's national assembly has voted to let priests bless same-sex marriages and civil partnerships while continuing to ban church weddings for those couples.

Bishops proposed the compromise measure after five years of discussions about the church's position on sexuality.

It was approved by the church's General Synod, which is made up of bishops, clergy and laypeople from around the country, following eight hours of debate over two days at a meeting in London.

The measure included an apology for the church's failure welcome LGBTQ people.

But it also endorsed the doctrine that marriage is between one man and one woman, meaning priests are still barred from marrying same-sex couples.

"I know that what we have proposed as a way forward does not go nearly far enough for many, but too far for others," the Bishop of London Sarah Mullally said in a statement.

"It is my prayer that what has been agreed today will represent a step forward for all of us within the church — including LGBTQI+ people — as we remain committed to walking together."

Jayne Ozanne, a gay rights campaigner and member of the synod, said she was "deeply disappointed" that conservatives had stifled the church's debate on sexuality.

The synod earlier this week rejected an amendment proposed by Ms Ozanne that would have put the issue of marriage equality back on the agenda later this year.

"By continuing to tell LGB people that they cannot hope to get married any time soon in their church or that their desire for sexual intimacy is sinful, we send a message to the nation that few will understand," Ms Ozanne said on Twitter.

Same-sex marriage has been legal in England and Wales since 2013, but the church did not alter its teaching on marriage when the law changed.

Public opinion surveys consistently show that a majority of people in England support same-sex marriage. But the Archbishop of Canterbury Justin Welby said the church continued to have "deep divisions" on the issue.

The measure approved on Thursday endorses a proposal from the church's bishops to allow clergy to bless the unions of same-sex couples after they marry or have a partnership recognised by civil authorities. But clergy members will not be required to perform such blessings if they disagree with them.

The blessings are expected to begin later this year after the bishops refine their guidance and issue prayers for the clergy to use.

Archbishop Welby said last month that he wouldn't personally bless any same-sex couples because it's his job to unify the 85 million members of the Anglican Communion around the world.

Archbishop Welby is the spiritual leader of both the Church of England and the global Anglican church of which it is a member.

He still celebrated Thursday's decision.

"It has been a long road to get us to this point," he said in a statement issued jointly with the Archbishop of York Stephen Cottrell.

AP