To rephrase (for clarity) the original question a bit, I suppose it's more "What is the most high-brow sitcom in terms of its setting and content?"
To which I still can't think of a better answer than Yes Minister and Yes, Prime Minister. There have been some which have been close in terms of setting (Chambers, The New Statesman, No Job For A Lady, even Is It Legal?, spring to mind), and some very clever in their content (I suppose this part of it is where H2G2 comes in), but I'm struggling to think of anything else that pairs the two as well as YM/Y,PM.