Although best known for playing the henpecked Richard Bucket in Keeping Up Appearances (1990), Swift eventually grew tired of being recognised for this role.
He appeared under the direction of Alfred Hitchcock in Frenzy (1972) and, over thirty years later, played Hitchcock in a British radio play.
He was previously a teacher at LAMDA and the Royal Academy of Dramatic Art.
Of his appearance in the 2007 Doctor Who Christmas special, Swift declared "It wasn't until we'd been filming for two weeks that I realised that Mr Copper is an alien!".
He had one daughter, Rebecca, and two sons, Adam and Joseph.
He was previously a director of The Royal Academy of Dramatic Art (RADA).
Educated at Clifton College and Gonville and Caius College, Cambridge.