The three-part BBC series was also voted as the Best Drama Series in the most coveted award for television industry, the British Academy of Film and Television Arts.
"I know it's very fashionable to say you don't care about this stuff but I'm very chuffed," ContactMusic quoted the 39-year-old as saying.
The other winners at the award ceremony were actor Steve Coogan who accepted the Best Male Comic Performance for "The Trip", while comedienne Jo Brand won the female equivalent for hospital sitcom "Getting On". The Best Actor award was given away to Daniel Rigby, for playing the lead in "Eric and Ernie".
The prestigious ceremony, held at the Grosvenor House in London Sunday, was hosted by Graham Norton.
