Curram was educated at Brighton College and has had a long film, television and theatre career. His appearances include Julie Christie's travelling companion in her Oscar-winning film Darling and expatriate Freddie in the BBC soap opera Eldorado. He is the author of three novels:- Man on the Beach published 2004 by Matador, The Rose Secateurs (2007) and Mother Loved Funerals (2010). In 1979 he played Brian Pilbeam in the first series of Terry and June. The Pilbeam's were Terry and June's annoying neighbours until the Spry's moved in.
He also starred as Harold Perkins in the acclaimed BBC TV series Big Jim and the Figaro Club which was broadcast in July and August 1981.
He was married to the actress Sheila Gish from 1964 until 1985, by whom he had two daughters, the actors Kay Curram and Lou Gish (1967–2006). Curram came out as gay in the early 90s.