Plowright was born, the daughter of Daisy Margaret (née Burton) and William Ernest Plowright, who was a journalist and newspaper editor. She attended Scunthorpe Grammar School and trained at the Bristol Old Vic Theatre School.

Plowright made her stage debut in 1951 and her London debut in 1954; she was long known as a superb theatre actress.

In 1956 she joined the English Stage Company at the Royal Court and won the role of Margery Pinchwife in The Country Wife. She appeared with George Devine in the Eugène Ionesco play, Les Chaises, Major Barbara, Saint Joan.

In 1957 she co-starred with future husband Sir Laurence Olivier in the original London production of John Osborne's The Entertainer, taking over the role of Jean Rice from Dorothy Tutin when the play transferred from the Royal Court to the Palace Theatre.

Plowright continued to appear on stage and in films such as The Entertainer (1960) and The Three Sisters (1970). In 1961 she received a Tony Award for her role in A Taste of Honey on Broadway. After a brief hiatus to devote time to her family she returned to the screen and can be seen in films such as Dennis the Menace, a cameo in Last Action Hero, Enchanted April, for which she won a Golden Globe Award and an Academy Award nomination, and Tea With Mussolini.

She was also notable for her major roles in 101 Dalmatians and Balto. Among her television roles, she won another Golden Globe Award and earned an Emmy Award nomination for the HBO film "Stalin," as the Soviet dictator's mother-in-law.