In an interview with the Sunday Times, Bishop Conry said: 'I've never regretted being a priest. I've never felt unhappy, I've enjoyed it and tried to do whatever was asked of me.
'I've always gone where I've been sent and I hope to do the same again.'
The affair was exposed when Simon Hodgkinson hired a private detective to follow his wife, Olivia, when their marriage broke down.
A second love affair six years ago also came to light and yesterday there were claims of a third woman in his life.
The bishop decided to resign because it 'was the easiest way to avoid further embarrassment, disappointment...and shame for the church.'
In his resignation statement he made a point of saying his actions 'were not illegal and did not involve minors.'
Mr Hodgkinson realised his wife was being unfaithful when she failed to turn up for choir practice at their local church.
The City executive said: 'I thought it was odd when she didn’t arrive at choir practice because normally she would never miss one. I went to her house to drop some music through her letterbox but she wasn’t at home.
‘By then it was about 10pm and I thought it was really weird. I decided it was time to test my suspicion that she was having an affair.
‘I went up to the bishop’s residence and her car was there. I checked and it was there all night. I was devastated.
‘I thought the bishop was someone who was honest and liberal. He is a man who has trained marriage counsellors – and is someone I had seriously thought of turning to for advice in relation to my own marriage.
‘Now, because he was such a powerful public figure, I could not go to anyone in the Church. I wanted to protect my family, I wanted to protect the children but I did not know what to do.’
The scandal has come at a time when the church is under growing pressure to consider relaxing its requirement for priests to remain celibate and to allow married men to become ordained.
Bishop Conry told Margarette Driscoll, of the Sunday Times: 'When a priest makes a promise of celibacy, he promises to remain unmarried, that's all. Then the ordinary rules of morality apply.
'But I'd like to make it clear I'm not calling for a change. I did wrong. Celibacy may be a tradition rather than an article of faith but the vast majority of priests are faithful to their promise, faithful to what the church expects of them. And I have great respect and admiration for that.'
