OneBodyOneFaith spoke out after the clergy, who include the bishops of Durham and Carlisle, wrote an open letter to the Bishop of Coventry who is chairing the Church of England's 'Living in Love and Faith' (LLF) project.
In the letter, they warned of "major problems" and the danger of division if the Church changes its current position.
They said that the traditional Christian view of sex as being for heterosexual marriage alone "is the teaching of Scripture" and "therefore expresses the character and will of God".
Responding to the letter, OneBodyOneFaith accused the bishops of being out of touch with UK evangelicals.
In a statement, it said: "What may come as news to these bishops is that the evangelical world has moved on - indeed, perhaps this letter arises out of the fear of recognising just this reality.
"They no longer speak for all evangelicals; their sisters and brothers still hold their evangelical identity dear but have been courageous and open-hearted enough to see a bigger God emerge, God powerfully alive in LGBTI+ people and longing to be known as good news for all, without exception."
In a call for change within the church, the group said: "Over the coming weeks and months, it will be for the other members of the House of Bishops, in all their diversity of opinion, to hold these eleven of their sisters and brothers to account.
"But ultimately we must all answer before God for those we have drawn to faith, and perhaps especially for those we have turned away, blocking the movement of the Spirit and diminishing the Body of Christ."
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