The Church of England met a mixed response after dropping its ban on clergy in civil partnerships becoming bishops.
Human rights campaigners welcomed the move, which would allow gay clergy to become bishops if they promise to be celibate. However critics said it was "unenforceable" and could prove divisive, not only in England, but within the Anglican Communion.
The decision was announced before Christmas but spotlighted on Friday in the Church Times newspaper.
A summary of business conducted by the House of Bishops when it met last month included that they lifted the moratorium on the appointment of clergy in civil partnerships as bishops - as long as they are celibate. The move comes after the General Synod controversially rejected proposals to allow women bishops in November.
Ruth Hunt, director of public affairs for gay rights campaigners Stonewall, said: "We're sure many Anglicans will be happy to hear of the Church's latest epiphany on gay clergy, although many lesbians will be disappointed that they remain unable to serve as bishops. I'm sure celibate gay men will be thrilled by this exciting new job opportunity, if perhaps somewhat perplexed as to how it will be policed by the Church."
Human rights campaigner Peter Tatchell said: "The announcement that gay clergy in civil partnerships will no longer be barred from appointment as bishops is a welcome move towards greater equality within the church. However, the restriction that they can be only appointed if they remain celibate is continued discrimination.
"Many are in loving, stable, long-term same-sex relationships that are akin to marriage. The church should welcome love, fidelity and commitment, regardless of whether its bishops are heterosexual or homosexual. This new policy did not exist when Jeffrey John was barred from becoming a bishop. Hopefully, the way is now clear for his appointment. His exclusion was a grave injustice against an outstanding theologian."
Dr John, Dean of St Albans, is the most senior openly gay Church of England cleric. He was reportedly forced to withdraw his acceptance of the post of bishop of Reading in 2003 after protests from traditionalists. It has also been claimed that he was blocked from being appointed as bishop of Southwark in 2010. Dr John entered a civil partnership in 2006, but is understood to live a celibate life.
The Rev Rod Thomas, a spokesman for Reform, an evangelical network in the Church of England, said: "It's a very worrying development. If someone were to be appointed who was in a civil partnership, that would be a very divisive step, both within England and across the Anglican Communion.
"Although the Church says they would be required to declare that they are celibate as part of their appointment, the fact is that this is unenforceable... If it's unenforceable for the clergy, it will be unenforceable for bishops. To appoint someone in a civil partnership as a bishop would be seen by the world at large as appointing someone who is in an active gay relationship, and undermine the Church's teaching on the exclusiveness of sex within marriage."