British police said in February that a 68-year-old man had been arrested as part of an investigation into an allegation that a man was sexually assaulted between 2018 and 2025. Conway was released on conditional bail.
The Church of England said that a safeguarding complaint concerning Conway had been referred to the relevant authorities.
A member of parliament's upper house, the House of Lords, Conway became Bishop of Lincoln in 2023. He was among a number of clergy criticised in an independent review into the Church of England's handling of prolific abuser John Smyth, though he said at the time that he had done all he could within his authority.
His resignation comes as the Church continues to face scrutiny over safeguarding failures following the fallout from the Smyth review, which in 2024 led to the resignation of Justin Welby, the then-Archbishop of Canterbury.