| Year | Award | Category | Work | Result | Ref. |
| 2015 | FilmQuest Awards | Best Actor | SuperBob | Won | |
| Best Screenplay (shared with Will Bridges and Jon Drever) | Won |
| 2016 | British Independent Film Awards | Best Supporting Actor | Adult Life Skills | Won | |
| 2021 | Gold Derby Awards | Comedy Supporting Actor | Ted Lasso | Nominated | |
| Hollywood Critics Association TV Awards | Best Supporting Actor in a Streaming Series, Comedy | Won | |
| International Online Cinema Awards | Best Supporting Actor in a Comedy Series | Won | |
| Screen Actors Guild Awards | Outstanding Performance by an Ensemble in a Comedy Series (shared with cast) | Nominated | |
| Primetime Emmy Awards | Outstanding Supporting Actor in a Comedy Series | Won | |
| Writers Guild of America Awards | Television: Comedy Series (shared with other writers) | Won | |
| Television: New Series (shared with other writers) | Won | |
| 2022 | Critics' Choice Television Awards | Best Supporting Actor in a Comedy Series | Won | |
| Golden Globe Awards | Best Supporting Actor – Series, Miniseries or Television Film | Nominated | |
| Screen Actors Guild Awards | Outstanding Performance by a Male Actor in a Comedy Series | Nominated | |
| Outstanding Performance by an Ensemble in a Comedy Series (shared with cast) | Won | |
| Primetime Emmy Awards | Outstanding Supporting Actor in a Comedy Series | Won | |
| National Film Awards | Best Screenplay (shared with Catherine Tate) | The Nan Movie | Nominated | |
| 2023 | Primetime Emmy Awards | Outstanding Supporting Actor in a Comedy Series | Ted Lasso | Nominated | |
| Screen Actors Guild Awards | Outstanding Performance by a Male Actor in a Comedy Series | Nominated | |
| Outstanding Performance by an Ensemble in a Comedy Series (shared with cast) | Nominated |