Elphick grew up in Chichester, Sussex, where his family had a butcher’s shop. He was educated at Lancastrian Secondary Modern Boys School in Chichester, where he took part in several school productions including Noah and A Midsummer Night’s Dream. He initially considered joining the Merchant Navy and helped out in his local boatyard during school holidays. It has been reported that he stumbled upon acting by chance when, at the age of 15, he took a job as an apprentice electrician at the Chichester Festival Theatre while it was being built. He gained an interest in acting whilst watching stars such as Laurence Olivier, Michael Redgrave and Sybil Thorndyke. Olivier advised Elphick to go to drama school and gave him two speeches to use at auditions. Elphick was offered a number of places but decided to train at the Central School of Speech and Drama in Swiss Cottage (aged 18), because Olivier had attended there. After graduating from drama school Elphick was offered roles primarily as menacing heavies. He made his debut in Fraulein Doktor (an Italian-made First World War film circa 1968). He went on to play the Captain in Tony Richardson’s version of Hamlet (1969); landed parts in cult films such as The First Great Train Robbery and The Elephant Man and appeared in Lindsay Anderson’s allegorical O Lucky Man! (1973). He was also seen as Phil Daniels’s father in the cult film Quadrophenia (1979), as Pasha in Gorky Park (1983) and as the poacher, Jake, in Withnail & I (1987). In 1984 he played the lead, Fisher, a British detective recalling under hypnosis a dystopian, crumbling Europe and his hunt for a serial killer in Lars von Trier’s Palme D’Or nominated debut film, The Element of Crime.

On stage, Elphick played Marcellus and the Player King in Tony Richardson’s stage version of Hamlet at the Roundhouse Theatre and on Broadway and he later played Claudius to Jonathan Pryce’s Hamlet at the Royal Court Theatre, directed by Richard Eyre. In 1981 he appeared in the Ray Davies/Barrie Keeffe musical Chorus Girls at the Theatre Royal, Stratford East and he was also seen in The Changing Room, directed by Lindsay Anderson, at the Royal Court Theatre. His last West End stage appearance was in 1997 as Doolittle in Pygmalion directed by Ray Cooney at the Albery Theatre. However, it was for his television roles that Elphick became best known. He briefly appeared in Coronation Street (1974) as Douglas Wormold, son of the landlord Edward, who for many years owned most of the properties in the road. Douglas unsuccessfully tried to buy the Kabin newsagent’s from Len Fairclough. In 1979 he appeared in Crown Court as Neville Griffiths QC, prosecuting the daughter of the Selsey family for harming her abusive father. He was the only actor in that three-part story correctly to pronounce “Selsey” as “Zell-Zey”, in the manner of the West Sussex village near where his mother lived in Chichester. He played one of the main roles in the film Black Island in 1978 for the Children’s Film Foundation, played a villain in The Sweeney episode “One of Your Own” (1978) and played a policeman in The Professionals episode “Backtrack” (1979) and had a minor role in Hazell (1979), and appeared in the Dennis Potter play Blue Remembered Hills (1979). Elphick took the title role in Jack Pulman’s drama Private Schulz (1981). Here he played Gerhard Schulz, a German soldier conscripted into SS Counter Espionage during the Second World War to destroy the British economy by flooding it with forged money. He appeared as the Irish labourer Magowan during the first series of Auf Wiedersehen, Pet (1983) and starred as Sidney Mundy in the ITV sitcom Pull the Other One (1984), before playing Sam Tyler in four series of Three Up, Two Down (1985–89). In 1986 Elphick landed his biggest television success, Boon (1986–92, 1995). He played Ken Boon, a retired fireman who opened a motorbike despatch business and later became a private investigator. Boon was very successful and ran for seven series, attracting audiences of 11 million at its peak. There was also a one-off episode screened in 1995, two years after it had been made. During breaks from Boon, Elphick continued to act in film with cameo roles in The Krays (1990) and Let Him Have It (1991), and in 1991 he played Des King in Buddy’s Song, starring Chesney Hawkes and Roger Daltrey.

In 1993 Elphick took the role of a former Fleet Street journalist running a Darlington news agency in Harry (1993, 1995). He played the alcoholic and ruthless Harry Salter, who frequently used exploitation and underhand tactics to get a story. This series however was less successful and it was soon cancelled. Elphick went on to play Billy Bones in Ken Russell’s televised version of Treasure Island (1995) and Barkis in David Copperfield (1999). In 2001 he joined the cast of EastEnders, where he played Harry Slater, a romantic interest for Peggy Mitchell (Barbara Windsor). The plotline indicated that Slater had sexually abused his niece, Kat Slater (Jessie Wallace), at the age of 13 and her “sister” Zoe (Michelle Ryan) was the daughter born to her when she became pregnant by him. Elphick’s heavy drinking began to affect his performances, so the character promptly left the series, and news of his death in Spain reached Walford four months later. On 7 September 2002, Elphick died of a heart attack complicated by his drinking problem. He had collapsed at his home in Willesden Green, London, after complaining of pains. He was rushed to hospital where he died. He was 55 years old, twelve days before his 56th birthday. His interment was located in Chichester Crematorium.