Fassbender was honoured for his portrayal of a sex addict in Shame, and his role in Jane Eyre, while Colman won the best actress award for her performance in Tyrannosaur, beating three-time Oscar winners Vanessa Redgrave, Rachel Weisz and Tilda Swinton.
Colman was delighted to win for her role as a battered wife in Paddy Considine's Tyrannosaur. She said: "To win things for this particular film feels pretty special because it's probably the best part I will ever get, so it's lovely that people have loved it just as much as I have."
It was the latest in a run of awards for the Peep Show star.
Colman said: "I'd like to be cool like lots of people and go 'Yeah, it's in the downstairs loo', but they're absolutely all over the mantelpiece, polished."
Stars including Doctor Who actor Matt Smith, Downton Abbey's Elizabeth McGovern and Birdsong's Clemence Poesy all turned out for the red carpet event held at the London Film Museum on the South Bank.
The award for best film went to Lynne Ramsay's We Need To Talk About Kevin, about a woman's attempt to come to terms with her son's involvement in an American high school massacre.
Others winners at the show, hosted by Green Wing star Stephen Mangan, included Irish film The Guard, which won the Peter Sellers award for comedy, and Senna, which was named best documentary.
And actor John Hurt picked up the first of two lifetime achievement awards.
Here is a full list of winners:
- Best Film - We Need To Talk About Kevin
- Best Actor - Michael Fassbender for Shame and Jane Eyre
- Best Actress - Olivia Colman for Tyrannosaur
- Most Promising Newcomers - Tom Kingsley and Will Sharpe for co-writing and directing Black Pond
- Peter Sellers Award For Comedy - The Guard
- Best Documentary - Senna
- Best Screenplay - Andrew Haigh for Weekend
- London Film Museum Award for Technical Achievement - Robbie Ryan for his cinematography of Wuthering Heights
- Alexander Walker Special Award - John Hurt for his contribution to cinema
- Blockbuster of the Year, People's Choice Award - Harry Potter And The Deathly Hallows: Part 2.
SLIDESHOW: The stars on the red carpet...