I can second Spy - really very surprisingly intense.
Spaced and Black Books are my two new favorite British comedies, and they’re both quite recent. If you liked Shaun of the Dead, Spaced is pretty much the same team.
Little Britain, on the other hand, is one of the worst shows I’ve ever seen. IMHO, of course.
Good call - I haven’t caught it in quite a while (I think a new series has just started?) so didn’t think of it…
Little Britain can be very funny on first viewing, but gets stale almost at once - most characters are one-gag ponies…
Grim
What about Coupling?
I strongly recommend Help if any U.S. station picks it up or BBC America shows it. The series was written by Chris Langham and Paul Whitehouse, who also are the main actors. Langham plays a psychologist, and Whitehouse plays all of the psychologist’s different patients. Very, very funny, IMHO.
If you’re a fan of Chris Morris style black humour, I can recommend Monkey Dust - a few culturally-specific references, and definitely not for kids, but still perceptive and entertaining.
Yep, started a couple of weeks ago 
Ooooh yes!! How did I forget!! Brilliant show.
One more - Marion and Geoff. So understated it’s almost not a comedy, yet it’s also heartbreakingly funny.
I’ve also been watching MI-5 recently, known in the UK as “Spooks”. Normally I can’t stand precinct shows (doctors, lawyers, cops), but this one grabbed me. The first few episodes were pretty “eh,” but once they
deep-fried one of the main characters’ faces before shooting her I figured I should watch the rest. I haven’t been disappointed.