She was born in the North London suburb of Finchley, to Edward Blume (the son of Jewish immigrants, originally named Blumenthal, from Russia and Latvia) and Elizabeth Grew (a descendant of Jewish immigrants from Poland originally named Griewski).

She is known for playing Shakespearean roles, as well as for appearing in movies, for example Charlie Chaplin's movie Limelight, Laurence Olivier's Richard III and The Spy Who Came in from the Cold and Look Back In Anger with Richard Burton and A Doll's House.

She had a love affair with Richard Burton, a fling with Laurence Olivier, and was married to both Academy Award winning actor Rod Steiger and the American author Philip Roth, both of which marriages ended in divorce. In her memoir, Leaving a Doll's House, she writes how Roth - with a lifelong terror of commitment - reserved the right in a brutal pre-nuptial agreement to terminate their marriage at any time and how he endlessly pinballed between gentleness and cruelty, one day sending her flowers for a fine performance and the next day serving her with separation papers. Such was her love for him, her passivity, and the pattern of her relationships, that she was unable to leave, always seduced again. The book records how Roth ended their life together, and effectively their marriage, whilst in hospital suffering from depression. A litany of her supposed unreasonable behaviour provided his ostensible reason but it hid a new affair.

She has a daughter, opera singer Anna Steiger, by her marriage to the late Rod Steiger.