The Church of England reopened discussion of the most divisive issue in Anglicanism last night by unexpectedly saying that openly gay men could become bishops, providing they are celibate.

The timing of the announcement took supporters and opponents of gay bishops by surprise, and the decision threatens to present incoming Archbishop of Canterbury, the Rt Rev Justin Welby, with renewed infighting in the Anglican Church over the issue of sexual orientation.

One leading conservative last night warned the U-turn would put the debate about women bishops in the shade and "finally divide the Anglican Communion completely".

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Although liberals largely welcomed the news, they also voiced concerns that gay clergy would still be expected to answer searching questions about the nature of celibacy – something their straight single counterparts are not expected to do. The consecration of gay clergy as bishops has caused deep divisions within the Church of England since Jeffrey John was forced to withdraw his candidacy for the bishopric of Reading in 2003, following an outcry by conservative evangelicals.

Yesterday's decision could pave the way for Dr John, now Dean of St Albans and one of the few openly gay but celibate clerics, finally to take up a senior position within the Church.

In 2005, the Church decided that someone in a same-sex civil partnership could become a priest as long as they were celibate, but said nothing about whether someone in the same position could become a bishop.

In 2011, with conservatives threatening to cleave the Church in two if any new appointments were made, senior Church leaders brought in a moratorium on any further elevation of a gay clergyman to the role of bishop.

Now the House of Bishops, the body responsible for official teachings, has reversed that ban by declaring that a civil partnership is not necessarily a bar to entering the episcopate.

It comes after weeks of embarrassing headlines for the Church on the issue of sexuality following the failure to approve legislation on women bishops in November and the announcement by the Government the following month that the Church would be exempt from gay marriage legislation.

The House of Bishops' decision, which was taken in December but only became common knowledge yesterday, effectively ends the ban on an openly gay man becoming bishop as long as he remains celibate.

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Dr Welby takes a conservative evangelical approach to homosexuality but the incoming Archbishop is unlikely to risk a direct conflict with the House of Bishops so early in his tenure. When his appointment was announced he said he was re-examining his views on gay relationships "prayerfully and carefully". Last night, the Bishop of Norwich, the Rt Rev Graham James, said: "The House has confirmed that clergy in civil partnerships, and living in accordance with the teaching of the Church on human sexuality, can be considered as candidates for the episcopate. The House believed it would be unjust to exclude from consideration for the episcopate anyone seeking to live fully in conformity with the Church's teaching on sexual ethics or other areas of personal life and discipline."

The bishop added that because of the controversy surrounding such appointments, any gay cleric looking to become a bishop would be expected to answer questions on the nature of their celibacy.

The move will cause waves way beyond Britain's borders. The Church of England acts as the spiritual head to the Anglican Communion – 80 million worshippers scattered across the globe who have increasingly divergent opinions on key issues such as women and homosexuality. The Rev Rod Thomas, chairman of the conservative evangelical group Reform, warned that any appointment of a gay bishop would create "huge divisions". "It will put the divisions over women bishops in the shade," he told The Independent. "If the Church goes ahead with this it would finally divide the Anglican Communion completely and would mean the Church of England would not be able to operate as it has done historically."

The Rev Sharon Ferguson, from the Lesbian and Gay Christian Movement, said the change was welcome. "This is good news that makes common sense," she said. "If someone in a civil partnership who fulfils the Church's teachings on sexual ethics can be ordained as a cleric they should be able to become a bishop. The whole ban originally was really quite farcical."

She added that only the appointment of an openly gay bishop would reassure her that the Church really had changed its policy. "The proof will be in the pudding," she said. "It's all well and good saying something, it's another thing entirely to actually to do it."

Symon Hill, a Christian writer and associate director of the Ekklesia think-tank, said the Church was still enforcing discrimination.

"Unfortunately this is being presented as progress but it's really another announcement of discrimination," he said. "It's saying straight bishops can have sex but gay bishops can't. Celibacy is a gift from God. Some people are called to it, other are not. It's not a second-best option for second-best clergy."