- In 2003, received Tony Award for Best Performance by a Leading Actress in a Play
- In 2000, received Emmy Award for Oustanding Supporting Actress in a Miniseries or Movie
- In 2000, received Screen Actors Guild Award for Outstanding Female Actor in a Television Movie or Miniseries
- In 2000, received Golden Globe Award for Best Supporting Actress in a Series, Mini-Series or Motion Picture Made for Television
- In 1999, received San Sebastian Film Festival Award for Lifetime Achievement
- In 1995, received OBIE Award for Performance
- In 1994, received Venice Film Festival Award for Best Supporting Actress
- In 1991, received CableACE Award for Supporting Actress in a Movie or Miniseries
- In 1991, received Evening Standard Award for Best Actress
- In 1989, received CableACE Award for Actress in a Miniseries or Movie
- In 1988, received London Critics' Circle Award for Best Supporting Actress
- In 1987, received New York Film Critics Circle Award for Best Supporting Actress
- In 1985, received London Critics' Circle Award for Best Actress
- In 1985, received National Society of Film Critics Award for Best Actress
- In 1984, received National Society of Film Critics Award for Best Actress
- In 1984, received Olivier Award for Best Actress
- In 1981, received Emmy Award for Outstanding Lead Actress in a Limited Series or a Special
- In 1979, received Evening Standard Award for Best Actress
- In 1977, received Academy Award for Best Supporting Actress
- In 1977, received Golden Globe Award for Best Supporting Actress
- In 1977, received Los Angeles Film Critics Association Award for Best Supporting Actress
- In 1969, received Cannes Film Festival Award for Best Actress
- In 1969, received Film Critics' Guild Award for Best Leading Actress
- In 1969, received National Society of Film Critics Award for Best Actress
- In 1967, received Evening Standard Award for Actress of the Year
- In 1966, received Plays and Players London Theatre Critics Award for Best Actress
- In 1966, received Cannes Film Festival Award for Best Actress
- In 1961, received Evening Standard Award for Actress of the Year
