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Father Christopher Lindlar of St Andrew's in West Street feels unable to accept women bishops into the Church of England and about 30 members of the church have also left with him.
After his surprise announcement at the morning Mass many people were crying and distraught as they left the church.
Fr Lindlar said: "I realise that my decision will grieve some, will be a shock to some, will anger some and that to others it will be a relief. For those things, I ask forgiveness."
He added that his decision to resign had been long and painful to make, but it had been clear that the Church of England would be ordaining female bishops which he believed was breaking with "holding fast to the faith."
Fr Lindlar added: "It has become clear to me that, for me, there is no future in the Church of England. It has turned down a path that I cannot follow."
Mike Carey, a member of St Andrew's, said he was surprised at the announcement, despite rumours and gossip about the possibility.
He added: "The resignation came as a great shock to me and to most of the congregation. There was weeping and wailing afterwards and people felt let down. The announcement knocked the stuffing out of us."
* For full story see the East Kent Mercury, March 3.