| Year | Award | Category | Work | Result |
| 1993 | BAFTA Scotland Awards | Best Actor – Film | Riff-Raff | Nominated |
| 1995 | Best Actor – Television | Cracker & Hamish Macbeth | Won |
| CableACE Awards | Supporting Actor in a Movie or Miniseries | Cracker | Nominated |
| 1996 | Awards Circuit Community Awards | Best Actor in a Supporting Role | Trainspotting | Nominated |
| Royal Television Society Awards | Best Actor | Hamish Macbeth | Won |
| 1997 | British Academy Film Awards | Best Actor in a Leading Role | The Full Monty | Won |
| BAFTA Scotland Awards | Best Actor – Television | Hamish Macbeth | Nominated |
| Best Actor – Film | Trainspotting | Nominated |
| Evening Standard British Film Awards | Best Actor | Face, Carla's Song & The Full Monty | Won |
| London Film Critics' Circle Awards | British Actor of the Year | Won |
| Salerno Shadowline Film Festival | Shadowline Award | | Won |
| Golden Satellite Awards | Best Supporting Actor – Drama | Trainspotting | Nominated |
| Screen Actors Guild Awards | Outstanding Performance by a Cast in a Motion Picture (with Mark Addy, Paul Barber, Deirdre Costello, Steve Huison, Bruce Jones, Lesley Sharp, William Snape, Hugo Speer, Tom Wilkinson & Emily Woof) | The Full Monty | Won |
| 1998 | British Academy Television Awards | Best Actor | Hamish Macbeth | Nominated |
| MTV Movie & TV Awards | Best Dance Sequence (with Mark Addy, Paul Barber, Steve Huison, Hugo Speer & Tom Wilkinson) | The Full Monty | Nominated |
| Sant Jordi Awards | Best Foreign Actor | The Full Monty & Go Now | Won |
| Golden Satellite Awards | Best Actor in a Motion Picture, Comedy or Musical | The Full Monty | Nominated |
| 1999 | British Academy Television Awards | Best Actor | Looking After Jo Jo | Nominated |
| 2000 | Fangoria Chainsaw Awards | Ravenous | Nominated |
| Irish Film & Television Awards | Angela's Ashes | Nominated |
| 2001 | Empire Awards | Best British Actor | Nominated |
| 2004 | Golden Satellite Awards | Best Actor in a Miniseries or a Motion Picture Made for Television | Hitler: The Rise of Evil | Nominated |
| 2006 | Primetime Emmy Awards | Outstanding Supporting Actor in a Limited or Anthology Series or Movie | Human Trafficking | Nominated |
| Gold Derby Awards | TV movie/Miniseries Supporting Actor | Nominated |
| Women's Image Network Awards | Outstanding Lead Actor in a Miniseries or a Movie | Won |
| 2008 | BAFTA Scotland Awards | Best Acting Performance in Film | Summer | Nominated |
| 2009 | Best Actor – Television | The Unloved | Won |
| 2010 | Gemini Awards | Best Actor in a Continuing Leading Dramatic Role | Stargate Universe | Won |
| 2015 | BAFTA Scotland Awards | Best Directing in Film or Television | The Legend of Barney Thomson | Nominated |
| Best Actor – Film | Nominated |
| Best Feature Film (with John G. Lenic, Kaleena Kiff & Brian Coffey) | Won |
| Behind the Voice Actors Awards | Best Male Lead Vocal Performance in a Video Game | Castlevania: Lords of Shadow 2 | Nominated |
| Edinburgh International Film Festival Awards | The Michael Powell Award for Best British Feature Film | The Legend of Barney Thomson | Nominated |
| 2016 | Monte-Carlo Comedy Film Festival | Audience Award | Won |
| 2017 | 20/20 Awards | Best Supporting Actor | Trainspotting | Nominated |
| BAFTA Scotland Awards | Best Actor – Film | T2 Trainspotting | Nominated |