Margaret Tyzack, a stalwart British actress who won myriad awards for her stage performances, including a Tony, but who was best known in the United States for her roles in the public television series “The Forsyte Saga” and “I, Claudius,” died Saturday in London. She was 79.

Her death was announced by her agent, Pippa Markham, who did not specify a cause.

Tyzack, was first and foremost a theater performer whose stage resume was long and formidable. She won a Laurence Olivier Award, the London equivalent of a Tony, for playing the boozy, fiercely distressed Martha in a 1981 revival of Edward Albee’s “Who’s Afraid of Virginia Woolf?”

She won another Olivier two years ago as Mrs. St. Maugham, the haughty grandmother of an unruly granddaughter, in Enid Bagnold’s emotionally incisive 1950s comedy “The Chalk Garden.”

Tyzack appeared twice in featured roles on Broadway. In 1983, as the Countess of Rousillon in “All’s Well That Ends Well,” she was nominated for a Tony. Her next Broadway role, in 1990, was Lotte Schoen, a travel agency bureaucrat who plays foil to a flamboyantly eccentric tour guide (played by Maggie Smith), in Peter Shaffer’s comedy “Lettice and Lovage.”

That production appeared first in London and was almost kept from opening in New York because of union rules that require special permission for the casting of foreign actors in Broadway productions, permission that is usually granted only to international stars of indisputable singularity or box-office drawing power.

Smith, who was given dispensation, refused to appear on Broadway unless Tyzack was also allowed to join the cast, arguing that their onstage chemistry and Tyzack’s gifts fulfilled the requirement of singularity. Actors’ Equity, the union, finally agreed. Frank Rich, writing in The New York Times, called Tyzack’s performance “flawless,” and she won a Tony for it.

Tyzack first came to prominence in 1967, when she appeared as Winifred, sister of Soames Forsyte, the lead character in “The Forsyte Saga,” a 26-week series produced by the BBC that traced the fortunes of an upper-middle-class British family through 40-some years on either side of the turn of the 20th century.

Tyzack also appeared in the title role of “Cousin Bette,” a BBC series based on the Balzac novel about a manipulative spinster, and in “I, Claudius,” based on Robert Graves’ novel about the life of the Roman emperor Claudius (played by Derek Jacobi). Tyzack played Antonia Minor, Claudius’ mother.

She appeared in a handful of movies, including two directed by Stanley Kubrick, “2001: A Space Odyssey” and “A Clockwork Orange.” More recently she appeared in Woody Allen’s “Match Point.”