Bishop Kieran Conry of Arundel and Brighton, chairman of the Department of Evangelization and Catechesis of the Bishops' Conference of England and Wales, said in a statement that he would step down "with immediate effect."
"I would like to reassure you that my actions were not illegal and did not involve minors," Bishop Conry said in a statement read out in parishes of his diocese at Masses Sept. 27 and 28.
"I want to apologize first of all to the individuals hurt by my actions and then to all of those inside and outside the diocese who will be shocked, hurt and saddened to hear this," he said.
"I am sorry for the shame that I have brought on the diocese and the church and I ask for your prayers and forgiveness," the bishop added.
The day after the statement was released, the Mail on Sunday, a London-based newspaper, carried an article that alleged that Bishop Conry was having an affair with a married mother of two, who was pictured leaving his home and shopping with him, but who was not identified.
The article revealed extracts from "love letters" between the 43-year-old woman and the bishop, leaked to the newspaper by the woman's husband.
The woman's estranged husband hired a private detective to track his wife, who accompanied Bishop Conry on outings to the ballet, the British Museum and a Matisse exhibition. He is threatening to sue church leaders, claiming they knew about the affair.
The bishop told the newspaper, however, that he was resigning in connection with an affair he had with another woman six years ago.
Bishop Conry told the Daily Mail in an interview published Sept. 29 that he felt "liberated" by the announcement.
"It has been difficult keeping the secret," he said. "In some respects I feel very calm. It is liberating. It is a relief."
He continued: "I have been careful not to make sexual morality a priority (in homilies). I don't think it got in the way of my job, I don't think people will say I have been a bad bishop. But I can't defend myself. I did wrong."
Bishop Conry, 63, a former director of the Catholic Media Office, was ordained bishop by Cardinal Cormac Murphy-O'Connor in 2001.