Smith began her career on stage as a student, performing at the Oxford Playhouse in 1952, and made her professional debut on Broadway in "New Faces of '56". For her work on the London stage, she has won a record six Best Actress "Evening Standard" Awards for "The Private Ear" and "The Public Eye" (both 1962), "Hedda Gabler" (1970), "Virginia" (1981), "The Way of the World" (1984), "Three Tall Women" (1994), and "A German Life" (2019). She received Tony Award nominations for "Private Lives" (1975) and "Night and Day" (1979), before winning the 1990 Tony Award for Best Actress in a Play for "Lettice and Lovage". She appeared in Stratford Shakespeare Festival productions of "Antony and Cleopatra" (1976) and "Macbeth" (1978), and West End productions of "A Delicate Balance" (1997) and "The Breath of Life" (2002). She received the Society of London Theatre Special Award in 2010.