Um, The Prisoner.
But seriously,what happened to* Little Britain*? It didn’t jump the shark, it was just getting warmed up?!
I don’t understand.
Odd that no one has mentioned One Foot in the Grave. Yeah, it did get a bit tedious, formulaic and repetitive, but it was still iconic and not worse than the bulk of US telly.
Those Graham Norton things have usually been pretty good, and Jools Holland has had some pretty good moments.
Ah, weird message board crap happened, and I had a lot longer post typed up. But basically,I was saying that my dumb illiterate ass could have provided two-three years more for The Prisoner, yet Doctor Who has persisted for generations for no real merit. Yeah, I said it. And I have enjoyed some Who. OMG, so many episodes with UNIT running around spewing…jargon…and random alien crap. And the companion pandering. The show didn’t know if it was 6 of one or half a dozen of another. It was shite. I am passionate about this because there was so much potential–in the same way the Prisoner pulled my heartstrings–but nearly always fell short and seemed like As the World Turns with antennas and stupid costumes. And they alienated (ha) Eccleston, who actually brought humanism back into it…
Never mind., sigh.
Rumpole of the Bailey
Blackadder
Sherlock with Jeremy Brett
Since I am British it would be threadshitting if I just pointed out the shows you’ve all missed.
However, and bearing in mind many of you are referring to Monty Python which originally broadcast back in the 1970s (1969 to 1974), there are some shows which were massive in the UK none of you have mentioned and I wonder whether they are unknown or just unpopular.
Monty Python’s Flying Circus was innovative and clever. It absolutely deserves it’s fame but here’s a dirty little secret. For simple laughter The Goodies (which running from 1970 to 1982 went directly against Monty Python) was actually far funnier. One person upthread has mentioned it. No one else?
Benny Hill No one has mentioned Benny. Is this political correctness or is it simply not funny to Americans today? I still laugh when he slaps the little bald man (Jackie Wright) on the head but am I condoning bullying?
But the really big beasts of British Comedy through the 1970s and 1980s were the comedy variety shows by Morecambe and Wise. They did a little singing, dancing and acted out comedy sketches. I guess the US equivalent would be Bob Hope (yes, I know he was British born). Their 1970s Christmas shows DEFINED Christmas for the UK. Literally it would be the top rated show on TV. Also worth mentioning is the similar The Two Ronnies. Another ratings smash year after year in the 1970s and 1980s.
Finally for comedy the recent big hit has been sitcom Only Fools and Horses 1982 to 2003 although after 1996 the occasional specials decreased in quality. At it’s peak one third of the UK population would sit and watch this. I know it has been mentioned by Americans on these boards before but I haven’t noticed it in this thread.
TCMF-2L
I’m surprised no one’s mentioned “Heartbeat.”
My list in no order:
Almost any BBC classic adaptation, favorites being:
1995 Pride & Prejudice
Persuasion with Amanda Root/Ciaran Hinds
Bleak House
David Copperfield
Oliver Twist
Great Expectations
Tess of the D’ubervilles
The Mayor of Casteridge
North & South
Drama Series:
Orphan Black
Broadchurch
MI5
Downton Abbey
Comedies:
Extras is the best comedy of all time, IMHO
Absolutely Fabulous
Monty Python
With the exception of Benny Hill, I don’t think any of these shows have been shown generally in the U.S. I’ve heard of the The Two Ronnies and Only Fools and Horses, probably on other British shows, but I’ve never seen them. Haven’t seen Benny Hill since the 1970s.
Top Gear
Monty Python FC
Mr. Bean
I, Cladius
Benny Hill, surprised this took so long to mention.
The Two Ronnies, yes, it was on here in the US but decades ago, I remember it from the 70’s.
I loved it but thought the OP was looking for current shows more than syndication. Otherwise somewhere between Python and Benny Hill I would have had to find room for Sister Wendy. She was informative and amusing in equal parts and nothing like her could ever quite make it on US broadcast/Network TV.
I was going to mention Benny Hill a while ago but, a) I thought he was a series of one-off specials and not a continuing series (not that that really matters), and b) I chickened out; didn’t want to seem even more low-brow than I already am. 
As penance, I offer this:
Peep Show
Mighty Boosh
No one’s mentioned my favorite yet: The Piglet Files.
I’ll also add my vote for *
Monty Python’s Flying Circus
Fawlty Towers
The Two Ronnies
Keeping Up Appearances
The Vicar of Dibley
The Prisoner
The Good Neighbors (aka The Good Life)
To the Manor Born
Whose Line is it Anyway?
*
Oh, and I mustn’t forget two old favorites from my childhood:*
The Champions
My Partner the Ghost (aka Randall and Hopkirk (Deceased))
*
Let me add that I haven’t missed an episode of Orphan Black, but I can’t list it among my favorites. Though I think the cast is great, I find the writing very uneven, and haven’t yet decided whether or not I’m going to keep up with the third series.
The Doc and the 'lock.
That is, Doctor Who, first and foremost, and Sherlock.
Peep Show
IT Crowd
Monty Python
Mitchell and Webb Look
Little Britain
The Office
Derek
Benny Hill
Whose Line is it Anyway?
Fuckity fuck, I forgot The Thick of It 
Ack! How could I forget Kingdom. I loved, loved, loved it. So sad that it just… ended, when we had only just learned—
Argh!!
And Lark Rise to Candleford’s a huge favourite in our house.
With the exception of Benny Hill (and I think The Goodies, briefly), I don’t think any of those shows aired anywhere in the USA other than on PBS, and that meant that a PBS station near you had to pay for the rights to air it.
The Two Ronnies - another one I forgot…
For those of you outside of the USA, note that episodes of The Two Ronnies that aired here were heavily edited. In most cases, the celebrity guests’ parts were cut out, so the show would fit into a 30-minute time slot. Pretty much every episode aired here consisted of: opening credits; the news; the opening sketch; another sketch, usually with just Barker; Corbett in his chair; the two of them in a musical number; closing joke from the desk; “And so it’s good night from me / And it’s good night from him. Good night.”
It was on PBS for a while. I must’ve only watched 1 or 2 episodes. To me it was just sillier.
This did air on a commercial Chicago station in the early 70s, along with “Doctor in the House” and “Up Pompeii”. I thought they were hilarious (and for the time and place, really naughty). BH was rebroadcast here recently, and I chased down the DitH videos on YouTube. They just didn’t hold up. I was disappointed. Maybe it’s just because I’m a lot older and jaded.
ISTR around that time a Brit told me we Americans thought BH was a genius because we only got his best episodes, and we’d change our minds if we saw all of him. FWIW.
They were broadcast on PBS in the '80s. I enjoyed them. But the ony thing I remember from M&W is their closing song. T2R is still funny, but not good enough to make my list. However, I saw their “four candles” video on YouTube (for the first time in my memory) and it was great.
My taste in British comedy was formed by LPs of Beyond the Fringe and then Cook and Moore as a duo. So Python was right up my alley.