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Award
| Year | Award | Category | Nomination |
| 2010 | Ian Charleson Awards | Special Commendation | Nominated |
| 2011 | Ian Charleson Awards | Third Prize | Won |
| 2011 | Ian Charleson Awards | Third Prize | Won |
| 2011 | Ian Charleson Awards | Third Prize | Won |
| 2012 | Ian Charleson Awards | Special Commendation | Nominated |
| 2015 | WhatsOnStage Awards | Best Supporting Actress in a Play | Won |
| 2017 | BAFTA TV Awards | Best Supporting Actress | Nominated |
| 2017 | Screen Actors Guild | Outstanding Performance by an Ensemble in a Drama Series | Nominated |
| 2017 | Glamour Awards | UK TV Actress | Won |
| 2018 | BAFTA TV Awards | Best Supporting Actress | Won |
| 2018 | Primetime Emmy Awards | Outstanding Supporting Actress in a Drama Series | Nominated |
| 2020 | Venice Film Festival | Volpi Cup for Best Actress | Won |
| 2020 | Alliance of Women Film Journalists | Best Actress | Nominated |
| 2020 | Houston Film Critics Society Awards | Best Actress | Nominated |
| 2020 | London Film Critics Circle Awards | Actress of the Year | Nominated |
| 2020 | London Film Critics Circle Awards | British/Irish Actress of the Year | Nominated |
| 2020 | San Diego Film Critics Society Awards | Best Leading Actress | Nominated |
| 2020 | St. Louis Film Critics Association | Best Actress | Nominated |
| 2020 | New Mexico Film Critics | Best Actress | Won |
| 2021 | Critics’ Choice Awards | Best Actress | Pending |
| 2021 | Golden Globe Awards | Best Actress in a Motion Picture – Drama | Pending |
| 2021 | Screen Actors Guild Awards | Outstanding Performance by a Female Actor in a Leading Role | Pending |
| 2021 | Santa Barbara International Film Festival | Virtuosos Award | Won |
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