The appointment of the bishop of Grantham was a "major error", the conservative Anglican group Gafcon has said.
Bishop Nicholas Chamberlain revealed he was gay and in relationship on Friday.
He was consecrated by the archbishop of Canterbury, Justin Welby - who has said he knew about the bishop's sexuality.
But Gafcon, a group which includes conservative Anglicans around the world, said there had been an "element of secrecy" in his appointment.
A statement from Gafcon said the news about Bishop Chamberlain would "exacerbate" divisions within the Church of England and the wider Anglican world.
http://www.bbc.co.uk/news/uk-37267148