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Dr Mark Beach, the former Dean of Rochester, is being allowed to stay in The Deanery until Easter despite being threatened with legal action to move out.
Dr Beach resigned from the church at the end of January and has since taken up a job at a London-based charity.
But some members of the cathedral community are angry that, despite resigning with immediate effect three years into a seven-year contract, he is still living in the five-bedroom listed house.
Dr Beach, who had not performed any official duties since last August, quit over concern following a family breakdown.
Canon Dr Philip Hesketh has been appointed acting Dean while a full-time replacement is found. Dr Hesketh said the appointment of Dean came with the house and after he resigned he was given a month to vacate the premises.
This expired on February 28 when he was given an extension until last Sunday.
Dr Beach told the Medway Messenger earlier this month he had nowhere else to live but was “actively looking for somewhere” not in Kent.
Dr Hesketh said it was now understood that he had until Easter to leave.