He was born Richard Ernest Parkes Bartram in London, England. He studied at Hendon School and was interested in acting from an early age. After serving in the Royal Air Force during World War II, he trained at the Royal Academy of Dramatic Art (RADA).
After graduating from RADA, Barton began his acting career in repertory theatre, appearing in productions at the Birmingham Repertory Theatre and the Old Vic. In 1949, he made his West End debut in a production of "Richard II". He went on to appear in many other West End productions, including "Hamlet", "Macbeth", and "Othello".
Barton also had a successful film career, appearing in films such as "The Dam Busters" (1955), "The Longest Day" (1962), and "The Charge of the Light Brigade" (1968). He also appeared in several television productions, including the BBC's "The Age of Kings" (1960) and "The Forsyte Saga" (1967).
In addition to his acting career, Barton was also a stage director and producer. He directed many productions for the Royal Shakespeare Company, including "Hamlet", "Macbeth", and "King Lear". He also directed several productions for the National Theatre, including "The Cherry Orchard" and "The Seagull".
Barton was married to the actress Anne Baxter from 1949 to 1951. He later married the actress Natasha Parry in 1960. He had three children: a son, Morgan, and two daughters, Demelza and Lucy.
Barton died of cancer on 5 April 2000 at the age of 74.