Brian Desmon Anthony Hannon (born 5 October 1936) is a retired Church of Ireland clergyman, who was Bishop of Clogher from 1986 to 2001. He is also the father of the singer and songwriter Neil Hannon, lead member of The Divine Comedy, who wrote the theme music for the situation comedy Father Ted.
Hannon was educated at Trinity College, Dublin and ordained in 1962. His first post was a curacy in Clooney; after which he was the incumbent at Desertmartin. He ministered in Derry from 1969 to 1982, during the time of the Troubles. He then moved to the Church of Ireland Diocese of Clogher, as rector of the Cathedral Parish of Enniskillen in County Fermanagh, Northern Ireland and became Dean of Clogher. He was raised to the episcopate as Bishop of Clogher in 1986.
He retired on 5 October 2001, his sixty-fifth birthday. On 21 November the Church of Ireland House of Bishops met in Dublin, where they elected his successor, Michael Jackson.