Top Gear

The Increasingly Poor Decisions of Todd Margaret is set in UK, but I don't know if it's a Brit show, sorry. It's funny, though.

If you like your action adventure

Strike Back (up to season 4 and counting)

http://www.imdb.com/title/tt1492179/

Blackaddar has been mentioned already. Mr. Bean is another great Rowan Atkinson show, too. Throw in Thin Blue Line for good measure.

I've always been fond of Keeping Up Appearances.

The Young Ones is one I haven't watched in a while but have fond memories of.

Monty Pythons Flying Circus and their movies, of course.

Father Ted is another great one.

Absolutely Fabulous, actually I need to rewatch this, too. I've never got around to watching the whole series.

Red Dwarf deserves another mention and if you like Chris Barrie in that you should also enjoy The Brittas Empire.

You've got quite a bit of Gervais' stuff on there so you should enjoy Life's Too Short with Warwick Davis, there's also the Karl Pilkington stuff like An Idiot Abroad and The Moaning Of Life.

Little Britain and Come Fly With Me are good, too. I recommend Come Fly With Me more out of the two.

For something a little more on the serious side there's Life On Mars. Be sure you get the UK version, of course.

Gah, there's so many more I can't think of right now...

Mr. Bean is great if you like all-out silliness.

Black Adder is another great comedy from Rowan Atkinson (aka Mr. Bean), with the same characters set in a different historical setting from season to season.

Benny Hill was way ahead of his time for being a dirty old man who always got his comeuppance.

From the few BBC shows ive seen on netflix I'd reccomend Jekyll and Survivors: Complete Seasons One & Two

Jekyll, which deals with dr jekyll and mr hyde concept with a bit of scientific approach. A man that is dealing with 2 personalities and has a family he wants to protect.

The other series is Survivors: Complete Seasons One & Two which is a really cool show on a deadly virus outbreak that wipes out the majority of mankind with a few scattered survivors.

Oh yeah id forgot also throw in a recomendation to Faulty Towers. I freakin love that show. So much so I had to buy it. Every episode is hilarious.

The Mighty Boosh!
and if you liked that you might try Snuffbox too
Oh and its gets compared to The Goodies from back in the 70s to - you should check that out

After Python Michael Palin and a couple of the others did a short story series called 'Ripping Yarns' which probably doesn't get mentioned as much as it should

The Avengers - it a bit like The Prisoners on less good drugs but still SOME drugs

Frankie Howard's Up Pompeii! - especially if you like Carry On films, but still check it out if you don't!

Crazy 'Did all his own stunts' physical comedy in 'Some Mothers Do 'Av 'Em'

Our original, British Shameless is worth a watch as is Skins, MisFits and Teachers, maybe Benidorn too, not sure how well that would would translate though

Then there's some classic comedies that were very much of their time, you might like to see a couple of eps to see if they take your fancy

'Allo, 'Allo - WWII French Resistance based comedy
Dad's Army - WWII Home Guard based comedy
Hi-De-Hi - 50's Holiday Camp
Are you Being Served? - 70s department store (actually made in the 70s and 80s)
Open All Hours - Northern Corner shop comedy

For Sketch Shows check out Harry Enfield and Friends (make sure its not the dodgy series with a different name he rushed out for Sky though) and The Fast Show, maybe Fist of Fun and The Mary Whitehouse Experience (into Newman and Baddiel in Pieces) too
Telly!

Really good ones that i watched are

Black Adder
The Vicar of Dibley
IT Crowd
Dr. Who
Survivors (i liked it)
Keeping up Appearances

Some excellent suggestions so far.

I'd add Coupling, the U.K. version of course. You can skip the 4th season, it just was not as good without Richard Coyle.

My absolute favourite Sherlock Holmes is Jeremy Brett in the Sherlock Holmes TV Series (1984-1994), especially the first three series (1984-1986). The shows stick very close to the original stories.

Doctor Snuggles! ;)

Inspector Morse
A Touch Of Frost
Prime Suspect
Silent Witness
Bergerac
The Midsommer Murders
Hornblower
Sharpe

That is one show I would have to pass on. I love women with British accents, but her voice really gets on my nerves. She was one of my least favorite of the Doctor's companions. I would just want to strangle the life out of her 5 minutes into the show.