In my view it comes down to fine craftmanship. A lot of the stars that you see in British sitcoms have been in the business for many years, appearing on stage or serving their apprenticeship in radio productions before making the transition to TV. A huge number of our present and past stars have started from their days in University rep companies.

Take a look at this list. Brits will know almost all of the names. Americans will probably know more than half.

Douglas Adams, Clive Anderson, David Baddiel, Sasha Baron Cohen, John Bird, Graham Chapman, John Cleese, Peter Cook, Michael Frayn, David Frost, Stephen Fry, Germaine Greer, Matt Holness, Alex Horne, Nicholas Hytner, Eric Idle, Clive James, Tim Key, Hugh Laurie, John Lloyd, Miriam Margoyles, Simon McBurney, Rory McGrath, Ben Miller, Jonathan Miller, David Mitchell, Neil Mullarkey, Trevor Nunn, Bill Oddie, Sue Perkins, Jan Ravens, Griff Rhys Jones, Peter Shaffer, Tony Slattery, Emma Thompson, Mark Watson, Robert Webb.

All of these names started their careers in the Cambridge Footlights Theatre Company. And this is just a very small selection of Footlights alumni. In addition to this teeming pool of performing talent many of our top scriptwriters cut their teeth in the same place and have worked with the artists long before they make it in TV.

And then of course there's the BBC. Even the most cynical among us recognise those three simple letters as standing for quality both in terms of performance and production. The BBC have given us so many top class shows. Some have already been mentioned and are as well known in the US as they are over here. But there are so many others.

How many Americans know about 'Only Fools And Horses' for example? Or 'Allo, Allo'? Both prime examples of the best in British sit-com. How about 'The Good Life'. Or 'Porridge'. (Or anything involving the late, great Ronnie Barker.) Or the wild anarchy that was 'The Young Ones'. If you don't know of those ones then you're still missing out on some of the best. Try to find a few episodes or clips online and you'll see what I mean.

Mr. Bean and Benny Hill made a huge impact stateside, yet many over here regard those as being near the bottom end of our comedy heritage with far too much emphasis on the slapstick. (I don't regard Benny Hill as a comedian at all. But he was a superb clown.)  

Then there's the ratings thing in America. If a show doesn't pull in the viewing figures it gets cancelled sharpish. Over here a lot of our best started very small with a late slot on BBC2. (Monty Python started that way.) Python had a very small but dedicated following for its first two series before it finally took off over here. Their viewing figures would have seen it cancelled after the third show of series one in America.
Maybe that's the secret. We treat our sit-coms like fine wine. Maybe the first episode or even the first series is not to our taste. But we don't throw out the barrel. We allow it time to mature in a quiet corner of the BBC and the taste grows on us.

(And I'm darned if I know what's happened to the text in this.)

Expert in computer code including, but not limited to, BTW; IIRC; IMHO; LMAO; BRB; OIC; ROFL; TTYL. Black belt in Google-fu.