| Year | Award | Category | Work | Result |
| 1968 | Tony Award | Best Actress in a Musical | Darling of the Day | Won |
| 1979 | Olivier Award | Best Supporting Actress | And a Nightingale Sang... | Nominated |
| 1985 | Olivier Award | Best Supporting Performance | Richard III | Nominated |
| 1988 | Olivier Award | Best Actress in a Musical | Candide | Won |
| 1989 | BAFTA TV Award | Best Actress | Talking Heads: A Lady of Letters | Nominated |
| 1991 | British Comedy Award | Best TV Comedy Actress | Keeping Up Appearances | Won |
| 1992 | BAFTA TV Award | Best Light Entertainment Performance | Keeping Up Appearances | Nominated |
| 1992 | Olivier Award | Best Actress | Talking Heads | Nominated |
| 1993 | BAFTA TV Award | Best Light Entertainment Performance | Keeping up Appearances | Nominated |