The IT Crowd: Funny show. If you work in the IT field you'll probably think it's one of the funniest shows ever (or not, I tend to be a bit odd in my tastes)
Top Gear: 3 Brits Driving REALLY expensive cars REALLY fast and making jokes the whole time.
Dr. Who: If you don't know I don't know where to start.
Torchwood: Spinoff of Dr. Who, X-Files-esque, but has a team, is based in the UK and theyknow that aliens exist
Hustle: Like Ocean's 11 as a TV show
There are also older shows from the UK which I like:
Chef!: Lenny Henry is funny as hell, I think Gordon Ramsey may have taken notes from this show.
'Allo 'Allo: British comedy/sitcom about the German occupation of a small town in France and how the locals try and help some British airmen return to England.
Black Adder: Mr. Bean talks, and he is hilarious, Dr. House is in season 2!
Red Dwarf: A slacker, a hologram, an evolved cat, an android and a loopy computer lost in space and time.
I know some of these shows already have threads, and there are probably more UK shows that I'm missing but this is the list off the top of my head.