Reform has issued a statement urging Church leaders to 'admonish' Rt Rev Dr Alan Wilson.
He recently released a book in which he claims one in 10 Church of England bishops could be secretly gay.
Last week he told Premier's News Hour: "We've been going round and round in circles for 30 years in this.
"I've been part of at least three rounds of facilitated conversation in the 35 years I've been ordained.
"Strangely enough, pretty much everyone else in British society has managed to get through it in a better way: people in the military, people in politics, people in the media.
"I think the Church has got itself into a right old twist on this one and we need to get ourselves out."
Reform, which describes itself as 'a network of individuals and churches promoting the gospel of Jesus Christ by reforming the Church of England', says he should face punishment for his remarks.
It criticised what it said was the "steady erosion of the Church's commitment to biblical authority - particularly in the field of sexuality".
In a statement, it outlined its issue with Bishop Alan: "The continued failure to admonish the Bishop of Buckingham, despite his refusal to uphold the teaching of the Church and guidance of the House on matters of sexuality, whilst also allowing him, without criticism, repeatedly to describe Conservative Evangelicals as homophobic, including those who themselves experience same-sex attraction but seek to live celibate, God-honouring lives."
The Church of England is still opposed to gay marriage, although there has been an intense, ongoing debate.
A 'shared conversation' is being carried out, looking into teaching on homosexuality.
Reform has told its members to no longer take part in the debate, which it has described as 'deeply flawed'.
The group's also condemned the "lack of a consistent and clear response to those clergy who have entered into same-sex marriages".
It claims this 'pre-empts' the outcomes of the debate.
The Church of England has yet to respond.