| Year | Award | Category | Work | Result | Ref. |
| 2014 | Ian Charleson Awards | Best Performance in a Play | Romeo & Juliet | Nominated | |
| 2019 | MTV Movie Awards | Best Breakthrough Performance | Sex Education | Nominated | |
| Best Kiss (with Connor Swindells) | Nominated | |
| BAFTA Scotland Awards | Best Actor in Television | Nominated | |
| Edinburgh International Television Festival | Best Breakthrough Talent | Nominated | |
| 2020 | Newport Beach Film Festival | Breakthrough Artist Honouree | Won | |
| Broadcasting Press Guild Awards | Best Actor | Nominated | |
| Best Breakthrough | Won | |
| Royal Television Society Awards | Comedy Performance (Male) | Won | |
| Young Scot Awards | Entertainment | Won | |
| BAFTA Television Awards | Best Male Comedy Performance | Nominated | |
| BAFTA Scotland Awards | Best Actor in Television | Won | |
| Rose d'Or | Performance of the Year | Won | |
| 2021 | BAFTA Television Awards | Best Male Comedy Performance | Nominated | |
| 2022 | National Comedy Awards | Outstanding Supporting Role | Won | |
| Critics' Choice Television Awards | Best Supporting Actor in a Comedy Series | Nominated | |
| NME Awards | Best TV Actor | Nominated | |
| BAFTA Television Awards | Best Male Comedy Performance | Nominated | |
| BAFTA Scotland Awards | Best Actor in Television | Nominated | |
| Audience Award | Nominated | |
| 2024 | BAFTA Cymru Awards | Actor | Doctor Who | Won | |
| 2025 | Critics' Choice Television Awards | Best Actor in a Drama Series | Nominated | |