I spend many hours each day listening to classic BBC radio comedy. (Round the Horne, Beyond Our Ken, The Navy Lark, I'm Sorry I'll Read That Again, I'm Sorry I Haven't a Clue, Take It From Here, The Men From the Ministry, Hancock's Half Hour etc, etc).
ROK Radio has two channels devoted exclusively to British radio comedy and also includes some similar content on their Old Time Gold channel. They usually publish schedules (in GMT, so you need to remember to add an hour at this time of the year) but there's a problem with displaying them at the moment, so it's a case of taking pot luck to see what's on until they get the problem sorted out:
http://rokradio.com/
British Comedy Radio has similar content but never publishes a schedule (so it's pot luck again):
http://www.abacus.fm/british-comedy.html
Goon Show Radio broadcasts episodes of The Goon Show 24 hours per day:
http://goons.fabcat.org/