Houston was born in Clydach Vale, Glamorgan, Wales. He served in the army during the Second World War, and was briefly a stand-up Comedian performing to Soldiers during the war. He made his first film appearance in The Blue Lamp in 1950.

Other credits included My Good Woman (1973–1974), A Horseman Riding By (1978), Inspector Morse, It Ain't Half Hot Mum, Minder and Doomwatch, as well as the recurring character "Det Supt Jones" in Softly, Softly. He has also appeared twice as different characters in Doctor Who — as "Professor Owen Watson" in The Hand of Fear (1976) and as "Colonel Ben Wolsey" in The Awakening (1984). He also played Brother Cadfael in a 1979 BBC Radio 4 adaptation of One Corpse Too Many. Houston has over two hundred television and film credits, dating back as early as 1950. Houston won a BAFTA Cymru special award in April 2008.

Houston had a role as "Duncan Thomas", literary agent, in the 1980s British sitcom Keep It in the Family. He appeared in a number of films including The Great Game. In the 1970s he played Lord Peter Wimsey's valet Bunter opposite Ian Carmichael in the teleplays of several of Dorothy Sayers tales. His performance was praised in the New York Times.

Houston is married to the Actress and model Shirley Lawrence and had two children. In May 2000 he unveiled a Mining Memorial in his native Rhondda at the Rhondda Heritage Park. He led the tributes to the thousands of miners who died and suffered during 150 years of mining in the South Wales coalfield. He released an autobiography titled Glyn Houston, A Black and White Actor in December 2009.