Simmons, who won an Emmy Award for her role in the 1980s miniseries The Thorn Birds, died on Friday at her home in Santa Monica, California, her agent Judy Page told the Los Angeles Times. She had lung cancer.
Already a beauty at the age of 14, Simmons, who was born in London, made her film debut in the 1944 British production Give Us the Moon after being spotted by Val Guest, the director.
Several minor films followed before David Lean, the British director, gave the actress her breakthrough role of Estella, companion to the reclusive Miss Havisham in the 1946 Great Expectations.
That was followed by the Black Narcissus and Olivier’s Oscar-winning Hamlet in 1948, for which Simmons was nominated as best supporting actress.
She was nominated for another Oscar, for best actress for The Happy Ending, in 1969 before moving to television roles in the Seventies, Eighties and Nineties.
Her career saw her act alongside some of Hollywood's greatest leading men.
Her other notable films included Elmer Gantry, with Burt Lancaster; Until They Sail, with Paul Newman; The Big Country with co-star Gregory Peck; Spartacus, also starring Kirk Douglas; This Earth Is Mine with Rock Hudson; All the Way Home with Robert Preston; Mister Buddwing, alongside James Garner; and Rough Night in Jericho with Dean Martin.
Simmons left Britain for Hollywood in 1950, accompanied by the actor Stewart Granger, her future husband.
They were befriended by Howard Hughes, the reclusive tycoon, who flew them to Tucson, Arizona, for a surprise wedding.
"When I returned from the honeymoon," Simmons told a reporter in 1964, "I learned that Hughes owned me — he had bought me from (the British producer) J. Arthur Rank like a piece of meat."
Simmons finally ended up suing Hughes for the right to make more prestigious films at other studios, and the result was Young Bess, where she played the young Queen Elizabeth I, The Robe, The Actress, The Egyptian and Desiree.
In the latter film, in 1954, she played the title role opposite Brando’s Napoleon.
The pair teamed again in 1955 for Guys and Dolls, the Samuel Goldwyn-produced musical in which Simmons plays Sarah Brown, a Salvation Army-style reformer conned into a weekend fling in Havana by gambler Sky Masterson.
In the Eighties and Nineties she appeared on television shows including Murder, She Wrote, In the Heat of the Night and Xena: Warrior Princess.
Simmons and Granger, who divorced in 1960, had a daughter, Tracy.
Shortly after her divorce, Simmons married Richard Brooks, who directed her in Elmer Gantry and in The Happy Ending. Their marriage, which produced a daughter, Kate, ended in divorce in 1977.