Bishop Kieran Conry of Arundel and Brighton has told the Daily Mail that he feels “relieved” he no longer has to keep his affair a secret.
The bishop announced his resignation in a letter that was read out at Masses over the weekend.
In the letter he admitted to being “unfaithful” to his promises as a priest, referring to a relationship “going back some years”.
Bishop Conry has also been accused of a second affair with a married parishioner.
A lawyer for the woman’s husband claimed he was considering legal action against the Church over a possible cover-up, saying Church leaders had “known for years that the bishop has been having affairs”.
Bishop Conry denied he had a sexual relationship with the married woman, though he admitted she did stay at his house.
On Sunday he told the Mail: “It has been difficult keeping the secret.
“In some respects I feel very calm. It is liberating. It is a relief. I have been very careful not to make sexual morality a priority [in his sermons]. I don’t think it got in the way of my job, I don’t think people would say I have been a bad bishop. But I can’t defend myself. I did wrong. Full stop.”
In his statement read out over the weekend the bishop said: “I am sorry to confess that, going back some years, I have been unfaithful to my promises as a Catholic priest. I would like to reassure you that my actions were not illegal and did not involve minors.
“As a result, however, I have decided to offer my resignation as bishop with immediate effect and will now take some time to consider my future.
“I want to apologise 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.
“I am sorry for the shame that I have brought on the diocese and the Church and I ask for your prayers and forgiveness.”