Baker was born in Varna, Bulgaria. His father was an English businessman and honorary vice consul and his mother a Red Cross nurse who moved to Bulgaria to help fight cholera. He attended Lancing College, Sussex; he then appeared as an actor in repertory theatre and at the Old Vic. Baker’s third wife, Louie Ramsay, who died earlier in 2011, played his onscreen wife Dora in The Ruth Rendell Mysteries. Baker was survived by five daughters (four from his first marriage, one from his second). Baker first made his name in The Dam Busters and his first starring role was in The Ship That Died of Shame with Richard Attenborough. This was followed by a string of Ealing films, and his film the 1950s swashbuckler, The Moonraker has been shown all over the world since 1958. However, over time, Baker became better known as a television actor. He was the second (to Guy Doleman) of many actors to portray the role of “Number Two” in the series The Prisoner, appearing in the series’ first episode. He appeared in his own TV comedy series Bowler. He was also in the first episode of Some Mothers Do ‘Ave ‘Em, playing a company boss interviewing the show’s hapless main character. In the acclaimed 1976 drama serial, I, Claudius, Baker played the emperor Tiberius Caesar. In the late 1970s, he starred as Inspector Roderick Alleyn in four adaptations of the mystery novels of Ngaio Marsh with New Zealand settings, in a production for New Zealand television. From 1988 to 2000, he played Inspector Reg Wexford in numerous television adaptations of mysteries by Ruth Rendell and this is probably the role for which he became best known. In 1993, following the death of his second wife, he married the actress Louie Ramsay, who played Mrs Wexford in the same television series.

He also appeared in The Baron, Survivors, Minder in Series 1’s You Gotta Have Friends, Coronation Street (as brewery owner Cecil Newton), in the Doctor Who story Full Circle and masterful turn as a pair of twins in a 2005 episode of Midsomer Murders titled “The House In The Woods”. Baker also appeared in the British comedy television series The Goodies’ episode “Tower of London” as the “Chief Beefeater”, as well as in the sitcom No Job for a Lady, and he is popularly known for playing Captain Benson, the James Bond ally in the film The Spy Who Loved Me and for playing Sir Hilary Bray, a heraldry expert, in On Her Majesty’s Secret Service. Later, when Bond, played by George Lazenby, impersonates Bray to gain access to Blofeld, Baker’s voice was dubbed in place of Lazenby’s to provide the accent. Baker also played an (uncredited) NASA engineer in You Only Live Twice. Ian Fleming considered Baker to be the ideal candidate to play James Bond in the films but the role went to Sean Connery because Baker had other commitments. He played a character called “Jamus Bondus” in an episode of 1970’s farcical sitcom Up Pompeii!. Baker’s first theatre work was in repertory at Deal, Kent. His major stage credits include a season with the Old Vic company (1959–61), where he played Bolingbroke in Richard II, Jack in The Importance of being Earnest and Warwick in Saint Joan. In 1965 he started his own touring company, Candida Plays, based at the Theatre Royal, Bury St Edmunds, Suffolk. He was Claudius in Buzz Goodbody’s celebrated, modern-dress Hamlet for the Royal Shakespeare Company in 1975.

In 1980 Baker wrote Fatal Spring, a play for television dealing with lives of poets Wilfred Owen, Siegfried Sassoon and Robert Graves; this appeared on BBC 2 on 7 November 1980. It won him a United Nations peace award. His other writing credits included four of the Wexford screenplays. Baker was the subject of This Is Your Life in 1995 when he was surprised by Michael Aspel during at photo shoot on board a boat at Port Solent on the Hampshire coast. Baker died on 7 October 2011 at the age of 80. He died of pneumonia, after a stroke.