The policy -- which was decided in December and announced Friday by the House of Bishops of the Church of England -- raised the possibility candidates for bishop may be questioned about their sex lives and whether they repent having had gay sex, The Daily Telegraph reported Friday.
Rob Thomas, of the evangelical group Reform, called the shift in policy "a very worrying development" and a "divisive step." He said a requirement that a gay bishop remain celibate would be "unenforceable."
The Rev. Colin Howard, who heads a group that pushes for the inclusion of homosexuals and transgendered people in the church, said the policy was "totally inappropriate" and "will be laughed at by the majority in the country."
The bishops said they would take no further action until Sir Joseph Pilling, a career civil servant who retired as permanent secretary of the Northern Ireland Office, completes a report on the church's attitude toward sexuality.
The church is already involved in a major row about female bishops. The General Synod narrowly rejected allowing women to become bishops, a change supported by Rowan Williams, the outgoing archbishop of Canterbury, and other church leaders.
The policy was issued on the same day the Rev. Gene Robinson, the first openly gay bishop in the Anglican Church, retired from his position in the Episcopal Church in New Hampshire.