A traditionalist Anglican group has voiced regret after an Anglo-Catholic bishop said he would convert to Rome.
The Bishop of Fulham, John Broadhurst, has become the fourth Anglican bishop to make the announcement.
He intends joining the Roman Catholic Church because of his opposition to the way the Church of England plans to introduce women bishops.
Meanwhile, a Kent Anglican congregation has become the first to take up the Pope's offer to convert to Catholicism.
The Pope created a special enclave in the Roman Catholic Church for Anglicans unhappy with their church's decision to let women become bishops.
The Catholic Group on the CofE's General Synod said it deeply regretted the decision by Bishop Broadhurst.
The bishop, who is the leader of the traditionalist organisation Forward in Faith, is the most significant Anglican so far to say he will convert to Catholicism.
He is currently the "flying bishop" charged with looking after traditionalist parishes opposed to women priests and bishops in the dioceses of London, Southwark and Rochester.
The Catholic Group said it was determined to stay in the Church of England and fight for a better deal for Anglicans who did not want to serve under women bishops.
BBC religious affairs correspondent Robert Pigott says the group's statement seems intended to counter any encouragement Bishop Broadhurst's announcement might give to traditionalist clergy to take up Pope Benedict's offer of a privileged place in the Roman Catholic Church.
Our correspondent says many traditionalist clergy are unhappy with the level of protection so far offered to them from serving under a woman bishop, but might hesitate in the face of a decision likely to cause them considerable personal hardship.
Bishop Broadhurst's statement came as it emerged that the traditionalist Anglo-Catholic congregation of St Peter's in Folkestone had become the first to begin the process of leaving to join the Roman Catholic Church.
The Pope has created a special enclave in the Roman Catholic Church for Anglicans unhappy with their Church's decision to let women become bishops.
Under his controversial offer, Anglicans could retain some of their practices and traditions.
The vote for St Peter's to convert took place at the end of September - perhaps encouraged by the Pope's visit to Britain - but it has only emerged now.
At the time of the visit the Archbishop of Canterbury - in whose diocese St Peter lies - joked that he and the Pope had at least two things in common, a fondest for cats, and a keenness to recruit Anglican clergy.
However, the initiative was taken by lay people, with the intention of converting as a group, our correspondent added.
It is thought unlikely they would be allowed to take their church with them.