Hundreds of Anglican clergy and laity have signed an open letter supporting gay bishops in the Church of England.

In what they have described as "A Love Letter to Gay Bishops", the signatories pledge to affirm the ministry of all bishops, regardless of sexual orientation, should they choose voluntarily to "come out" as gay.

It follows a warning by the campaigner Peter Tatchell, disclosed in Christian Today last week, that bishops known to be gay could be involuntarily "outed" if they do not do so themselves. The Bishop of Buckingham Alan Wilson estimates in a new book that as many as one in ten bishops could be gay.

The letter, organised through Facebook among members of Changing Attitude, a lobby working for the full inclusion of LGBT people in the Church of England, reads: "We write to assure those bishops who may choose to openly acknowledge their sexual orientation as gay or bisexual that you will receive our support, prayer, and encouragement."

The letter has been signed by about 300 Anglicans, mostly from the Church of England and including clergy and Bishop Wilson. Members of other churches, including the Methodist Church, have also signed up.

Bishop Wilson said: "Sexual orientation is a deeply personal matter, but I am sure that as colleagues find the confidence to be as real about sexuality corporately as I always find they are personally and individually it will be a blessing to the Church."

Rev Kate Bottley, the "Gogglebox" vicar from the Southwell and Nottingham Diocese, who also signed the letter said: "The role of Bishop is demanding and at times difficult, all our bishops deserve our encouragement, affirmation and prayers as they serve, and I am only too pleased to add my voice to this letter. I can only imagine how demanding the role of bishop is and so I am keen to offer my encouragement and support to all who serve in this way, especially those who choose to acknowledge their sexual orientation as gay or bisexual."

She added: "Woop! woop! for all the beautiful, hardworking, committed Bishops who have given so much for the Gospel."

Anglican theologian, Dr Susannah Cornwall, who writes and teaches on theology, sex and gender at the University of Exeter also signed the letter. She said: "There are gay and bisexual people present and active at every level of the Church of England, but, regrettably, the ministry of openly LGBT people is not always endorsed or encouraged. The lack of any publicly LGBT people in the House of Bishops perpetuates the mistaken perception that LGBT identity is incompatible with Christianity in general and episcopal ministry in particular. No-one should ever be forced to come out, or outed against their will. However, the Church of England's public discourses on sexuality sometimes belie the diversity of experience and belief that already exists within the institution. As signatories to this letter we express support for gay and bisexual members of the House of Bishops, affirm their ministry, and assure those who do choose to come out that they will find bountiful support and encouragement in this part of their journey."

Laura Sykes, editor of the online think tank Lay Anglicana and another signatory, said: "If the Church is to continue to be led by bishops who are appointed rather than elected, it is essential that the laity can trust them. Truth-telling on this issue would command trust and loyalty from the great majority of churchgoers. "