The political comedy won the Situation Comedy award, beating stiff competition from The Inbetweeners, Peep Show and Miranda. Meanwhile The Thick Of It's stars also picked up awards: Peter Capaldi won 'Male Performance in a Comedy Role' for playing foul-mouthed spin doctor Malcolm Tucker, whilst Rebecca Front picked up the female award for her role in the show as down-trodden MP Nicola Murray.
Upon accepting her award, and after thanking the cast and crew, Rebecca Front thanked her parents for helping her learn lines for the show. She joked: "I've got to tell you, you've never heard my mother reading as Malcolm Tucker!". Peter Capaldi, sporting a thick beard, joked: "as you can see, I'm sporting my 'please take me seriously' beard". He went on to say: "I really think I should single out the writers for praise, but I think they get far too much and it just encourages grown men to behave like students."
After thanking the BBC comedy department, Armando Iannucci jokingly thanked Nick Clegg "for completely destroying our plans for the next series." He added: "The plan had been for the show to go on for many, many series and in the final episode all the characters wake up and discover the Liberal Democrats... that's not going to happen". Iannucci then singled out producer Adam Tandy for special praise, saying: "without Adam The Thick Of It would not happen".
E4's comedy output also did well. The Inbetweeners won the 'YouTube Audience Award', which is the only BAFTA award chosen by members of the public.
The other success for E4 was Misfits, which won in the 'Drama Series' category. Robert Sheehan, who plays gobby Nathan in the comedy drama, said: "We genuinely didn't believe that the esteemed members of BAFTA would ever vote for a show that featured myself having sex with an 82 year old woman." He also added that now might be a good time to ask E4 how they'd feel about commissioning a third series.
In the night's other big comedy category, The Armstrong And Miller Show headed off competition from The Kevin Bishop Show, Stewart Lee's Comedy Vehicle and That Mitchell And Webb Look to win the 'Comedy Programme' award. Getting up on stage Alexander Armstrong said: "Bloody hell Ben - we won! We did have quite a good line saying all that matters is being nominated... but, balls."
However, sadly none of the entertainment awards went to comedic works this year. Stephen Fry, Harry Hill, Michael McIntyre lost out in the 'Entertainment Performance' category to Ant & Dec; whilst Britain's Got Talent beat Graham Norton, TV Burp and Charlie Brooker's Newswipe to claim the 'Lew Grade Entertainment Programme'. Graham Norton, who was hosting the show, jokingly pretended to sulk at this point, leading Simon Cowell - who was also given a BAFTA Special Award earlier in the night - to insincerely remind the comic in a cheeky way: "It's not about the winning, it's about the taking part."
Here is a backstage video with the cast and crew of The Thick Of It...
Summary of results:
Male Performance in a Comedy Role
Female Performance in a Comedy Role
YouTube Audience Award
Britain's Got Talent
The One Show
The X Factor
For a full list of winners and nominees see www.bafta.org