Allen was born in Nyasaland (now Malawi), where his father was a tobacco farmer. After his parents returned to Britain, he was evacuated to Canada during World War II where he remained to finish his education at McGill University in Montreal. He gained experience as a local radio broadcaster and appeared on television in plays and documentaries, before returning to Britain.
Returning to the United Kingdom in 1953, Allen made his film debut in Hitchcock's Dial M for Murder (1954). He subsequently appeared in character roles in many films, including Captain Clegg, The Wild Geese, The Sea Wolves and Who Dares Wins. He was also the lead actor in the Associated Rediffusion adventure series Crane (1963–65) and in the BBC-1 series Brett (1971). Allen played Moriaty's deputy Colonel Sebastian Moran in The Adventures of Sherlock Holmes and The Return of Sherlock Holmes.
He made regular appearances in ITC television series during the 1960s and early 1970s, including The Baron, The Champions and UFO, although he never had an ongoing role in any of these series. He made one episode of the Saint alongside Roger Moore in The Man Who Could Not Die broadcast July 1965 in the UK.
Allen also worked with the Royal Shakespeare Company in a number of stage roles, along with many BBC productions.
Allen's distinctive, authoritative voice was familiar across Britain, even amongst those who did not recognise him as an actor.
He narrated the British Government's Protect and Survive series of instructional videos in the 1970s; some of his lines in that production were re-recorded and sampled into the single Two Tribesby the band Frankie Goes to Hollywood. He was also the voiceover artist for Vic and Bob's comedy series Vic Reeves Big Night Out, The Smell of Reeves and Mortimer and Shooting Stars, and appeared in and voiced numerous commercials for house builder Barratt Homes and for the Ford Sierra, among many others. His voice-over work led him to start up his own business, running a very successful recording studio for voice-over work.
He also narrated the first series of Blackadder, and appeared in the last episode 'The Black Seal' as Edmund's arch-nemesis, Phillip of Burgundy - known to his enemies as 'The Hawk'.
He provided the narration (the voice of Captain Star) for the 1989 children's series TUGS. Allen remained uncredited for his work, which was revealed in an interview with the show's producerRobert D. Cardona.
In 2005, he became the voice of the British television channel E4, providing voiceovers for many of its idents and promotions. Some of the slogans are rather irreverent, and match the tone of the channel well, especially during the channel's recent campaigns. These include:
- Only we has got Six Chuffing Feet (to advertise the final series of Six Feet Under)
- Paris squashed against Britney in your gaff (to advertise The Simple Life and Britney and Kevin: Chaotic back-to-back; the word 'gaff' is British slang for 'house')
- Big Shiny Films in your Dinky Little Home (to advertise films)
- Chucking Spunky Tunes In Your Tellybox (to advertise E4 Music, the channel's music television strand)
- Shamelessly importing Cool Stuff (referring to shows including Lost and the aforementioned Six Feet Under)
- Watch the piggies squeal! (advertising Big Brother Diary Room Uncut)
Since his death, the E4 voice-overs have continued with Peter Dickson continuing in Allen's style. Dickson also recreated Allen's more serious style for a mock car commercial in an episode ofAshes to Ashes.
In 2005, he did an altered re-recording of the Two Tribes version of the Protect and Survive narration for German cover band Welcome To The Pleasuredome, which is featured in their live performances.
Also, not long before his death, he narrated parody versions of these films for Kerrang! TV.
He was also the voice of the Christian O'Connell Breakfast Show on XFM, the late show on 103.2 Power FM, Hirsty's Daily Dose on Galaxy Yorkshire and briefly Virgin Radio, until he fell ill early in 2006.
He died on 28 July 2006. He left a widow, the actress Sarah Lawson and two sons, Stephen and Stuart.