"Our beloved mother Lynn Rachel passed away peacefully after a seven-year journey with breast cancer," the BBC quoted her children as saying in a statement. "She lived, loved and worked harder than ever before. The endless memories she created as a mother, grandmother, writer, actor and friend will sustain us for the rest of our lives."
A private funeral is expected later this week, the BBC said.
Her death is the third tragedy to strike the Redgrave acting dynasty in little more than a year.
Redgrave's brother, Corin, died of prostate cancer last month and her niece, Natasha Richardson, died after a skiing accident in March 2009.
Born March 8, 1943, in London, Lynn Redgrave was the daughter of actor Michael Redgrave, who died in 1985, and actress Rachel Kempson, who died in 2003, and the younger sister of actress Vanessa Redgrave.
Lynn Redgrave studied drama at Queensgate School and had a well-established reputation for stage and screen roles when in the late 1970s she became popular in the United States for television appearances, including a situation comedy, "House Calls," in which she co-starred with Wayne Rogers. It had its debut in December 1979.
Her movie career began with roles in "Tom Jones" in 1963 and "The Girl with Green Eyes" in 1964. Then came "Georgy Girl," for which she won a New York Film Critics award as best actress in 1966 in a tie with Elizabeth Taylor's "Who's Afraid of Virginia Woolf?" as well as a Golden Globe Award and an Oscar nomination.
More than three decades later, she won a Golden Globe Award and another Oscar nomination in 1999 for best supporting actress for her role as the longtime housekeeper of "Frankenstein" director James Whale in "Gods and Monsters."
"The 3 1/2 decades since (my last Golden Globe) have humbled me," she told reporters backstage. "I've been up and down ... I've been out. I'm having a renaissance at age 55."
Her film credits also included Woody Allen's "Everything You Wanted to Know About Sex But Were Afraid to Ask," "The Deadly Affair," "Smashing Time," "The Virgin Soldiers," "Don't Turn the Other Cheek," "Every Little Crook and Nanny," "The Happy Hooker," "The National Health," "The Big Bus," "Peter Pan," "Kinsey," "The White Countess" and "The Jane Austen Book Club."
She is survived by her son Ben and daughters Pema and Annabel, as well as six grandchildren, her sister Vanessa and four nieces and nephews, the BBC said.