The signatories, who include at least 160 priests and several members of the Church's governing General Synod, pledge to "welcome and embrace" those bishops who decide to go public but strongly object to any attempt to involuntarily "out" anyone.

It follows the publication of a new book by the serving Bishop of Buckingham, the Rt Rev Dr Alan Wilson, last week which said that around one in 10 of his colleagues could be gay but unwilling to speak publicly.

The book sets out a theological argument for a major reassessment of the Church of England's teaching on homosexuality accusing the hierarchy of "hypocrisy" and "duplicity" on the subject.

Dr Wilson remarked that there are currently "said to be a dozen or so gay bishops" but that events had left many trapped behind "episcopal closet door".

The letter, disclosed today in The Sunday Telegraph, will reopen an intense debate within the Church over its stance on sexuality.

The Church of England officially teaches that any sexual relationship outside of traditional heterosexual marriage is "less than God's ideal" - an Anglican euphemism for "sin".

But the Archbishop of Canterbury, the Most Rev Justin Welby, has pledged to clamp down on homophobia in the Church of England.

Although Anglican clergy can be in same-sex civil partnerships, they must claim to be celibate if they wish to become bishops.

There are no openly gay bishops in the Church of England and the current Dean of St Albans, Dr Jeffrey John, who is in a celibate same-sex relationship, was twice forced to turn down promotion to the episcopate because of opposition linked to his sexuality.

The Rev Dr Keith Hebden, a priest from St Mark's and St Peter's Church in Mansfield, Notts, has been gathering signatures for the letter which will be formally submitted to the Church's House of Bishops.

Last night 282 Anglicans, 29 Methodists and around 25 members of other Christian Churches, as well as representatives of Jewish groups, has already signed the letter. Dr Wilson is among the signatories.

It acknowledges "growing pressure" on gay bishops to come out publicly but expresses strong opposition to any threat to "out" them.

"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 signatories pledge.

Bishops who have kept their sexuality secret have, they say, having borne a particular personal "cost" and could face "hostility by a vocal minority" if they were to go public.

But they add: "We have no doubt that the vast majority of Anglicans will welcome and embrace those of you who are gay or bisexual for your courage and conviction if you come out: weeping with you for past hurts and rejoicing in God's call as witnesses to Christ's transforming love and compassion.

"If you stand out we will stand beside you."

Rev Hebden said: "I'm a straight, white middle class man -- I'm not saying to particular individuals 'you should come out'.

"What this letter is saying is that if you feel it is the right thing, through your thought and prayer and conversations with people you love, there is an immeasurable number of people out there who will love and support you."

The Rev Colin Coward, director of the Anglican campaign group "Changing Attitude", said: "It is really important for bishops both straight and gay to live with integrity and openness about their identity and their beliefs about the full inclusion of lesbian and gay people in the church.

"Those of us who are lesbian and gay long to be supported by openly gay bishops and we know from our own experience how much energy and Christian integrity is released when you live openly with your sexuality."