Pope Benedict's offer has divided the Church of England
Some Anglican clergy have said they are ready to accept an offer to join the Roman Catholic Church at a meeting of about 600 conservative priests.
Members of the Forward in Faith group discussed the Pope's invitation to Anglicans to convert to Catholicism but keep many of their existing practices.
Many who are considering conversion are unhappy at women bishops being introduced into the Church of England.
Others at the meeting, in Westminster, urged their colleagues to stay.
They have pleaded with their colleagues to stay inside the Church and fight for a compromise that would allow them to live harmoniously with women bishops.
Under the terms of the invitation offered by the Vatican, those who convert could keep many of their Anglican traditions in their own special section of the Roman Catholic Church.
The Vatican said it was responding to pleas for help from Anglicans.
Some leading Anglicans have criticised the Vatican over the move.
The Former Archbishop of Canterbury, Lord Carey, said he was appalled that Rome had not told his successor, Dr Rowan Williams, about its plans until two weeks ago.
He said: "We mustn't be treated as a junior partner in this. It's got to be done in a serious way that respects each party and I was raising a question simply, 'Is that being done at the present moment?'"
Father Geoffrey Kirk, one of the leaders of Forward in Faith, is among those who said he intends to convert to Catholicism.
He said: "The Church of England is, in the view of many of us, ceasing to be the church of Jesus Christ and becoming the church of political correctness, not only the ordination of women to the priesthood and the episcopate - to which we object - but also in many attitudes to human sexuality from divorce and remarriage, to homosexuality."
Other Catholic-minded Anglicans warn that the Church of England could become more Protestant and more progressive if more conservative clergy accept the Vatican's invitation.
They want to preserve the historic role of the Church of England in uniting Protestant evangelicals on one side with others far more sympathetic to Catholicism - a point made by Father David Houlding.
He said: "It's not a Protestant church, pure and simple, that's not what the Church of England is - it never has been.
"I fear that if we moved into that direction exclusively, then the Church of England would not be in the position that it is at the moment to appeal to a wide variety of people."
BBC religious affairs correspondent Robert Pigott said the reaction to the offer made by Rome could have far reaching consequences.
He said: "For more than 500 years the Church of England has united Christians of radically different backgrounds - on the one hand evangelical Protestants, and on the other clergy who are much more sympathetic to the Catholic Church.
"If many of these Catholic-minded clergy take up the Pope's offer, it could alter the Church's character for ever."
Our correspondent added that there is likely to be intense pressure on the Church of England to find a compromise on women bishops, particularly since those who oppose them now have an easy route to Rome.