Jonathan Ross hosted the show, which aired live on Channel 4.
Alan Partridge star Coogan took home the Outstanding Achievement award, while Jack Whitehall received the King of Comedy accolade, as voted for by the public, for the second year running.
Mack had two reasons to celebrate, after he won Best Male TV Comic and Would I Lie To You - which he co-hosts with David Mitchell - was awarded the Best Comedy Panel Show trophy.
It was another double win for Paul Whitehouse, who was given the prestigious Writer's Guild of Great Britain Award and also celebrated winning the Best Sketch Show accolade alongside Harry Enfield for Harry & Paul.
Fresh Meat's Whitehall was awarded Best TV Comedy Actor, with Miranda Hart reclaiming her title as Best TV Comedy Actress after initially winning the award for her work on Miranda in 2011.
Best Comedy Entertainment Personality went to Alan Carr for Chatty Man, while Graham Norton picked up Best Comedy Entertainment Programme for The Graham Norton Show.
Nina Conti won her first British Comedy Award, scooping Best Female TV Comic for her performance on Live At The Apollo.
British Comedy Awards winners in full
British Comedy Awards 2013 in pictures
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