British comedy is widely produced by BBC TV and radio.

Radio 4 is in charge of the brilliant National Theatre of Brent series by Patrick Barlow/Desmond Olivier Dingle and starring him and Jim Broadbent/Wallace. They were also the originators of the legend that is The Hitch-Hikers' Guide to the Galaxy.

Other radio comedies include:Just a Minute,
I'm Sorry I'll Read That Again,
I'm Sorry I Haven't a Clue,
It's That Man Again,
The Navy Lark,
The Huddlines,
The Goon Show,
People Like Us (later to become a TV series),
and so many others.

BBC TV, apart from the comedies mentioned above, also made/makes/co-produced/co-produces:
Dad's Army,
It Ain't Half Hot Mum,
Steptoe and Son,
Only Fools and Horses,
Bread,
Monty Python (and the films),
Porridge,
Going Straight,
Men Behaving Badly,
The Royle Family,
Sorry,
Birds of a Feather,
Butterflies,
Upstairs Downstairs,
Hi-De-Hi,
Oh Doctor Beeching,
Hancock's Half Hour,
As Time Goes by,
Open All Hours,
The Two Ronnies,
the various Morecambe and Wise series,
Yes, Minister and Yes, Prime Minister,
The Fast Show,
We are History,
Keeping Up Appearances,
One Foot in the Grave,
Red Dwarf,
Room 101,
The League of Gentlemen,
Alan Bennett's Talking Heads,
Dinnerladies,
Mrs Merton,
Coupling,
Rex the Runt,
Have I Got News for You,
Never Mind the Buzzcocks,
Shooting Stars and the other Vic Reeves and Bob Mortimer series,
the various Smith and Jones series,
Men Behaving Badly,
the creations of the Chuckle brothers,
The Thin Blue Line,
Kiss Me Kate,
Perfect World,
Game On,
Call My Bluff,
the new show Chambers,
a new Scottish show Chewin' the fat,
and many, many more, but that's all I can think of for now.

As well as this, there are several British films that are very funny. Examples are:
the Carry On films,
The Full Monty,
the Wallace and Gromit short films,
Chicken Run, even though it was produced in America,
and more, but not so many nowadays. If you think of any more, please /msg me.