I listen to a lot of classic British radio comedy. (The Navy Lark, Round the Horne, Men from the Ministry, etc)
This is probably my favourite station:
http://www.abacus.fm/british-comedy.html
(They don't publish a schedule but regulars listens get toknow when their favourite programs will be on)
ROK has two British comedy channels. Schedules here
http://rokradio.com/program-schedule-british-comedy-channel/
and here
http://rokradio.com/british-comedy-radio/
There's also some comedy content on their Old Time Gold channel:
http://rokradio.com/program-schedule-old-time-gold/
24-hour Goon Shows can be found here
http://goons.fabcat.org/
and here
http://goonshowradio.radio.net/
RadioEchoes is a site hosting MP3 files, which can be either streamed or downloaded, of a vast number of old radio programmes. Many are American but for example, there are 247 episodes of The Navy Lark and 153 episodes of The Men From The Ministry there amongst the British content
http://www.radioechoes.com/bandaid/
The Old Time Radio Researchers Library is similar but with less British content (and without the ability to stream programs - you have to download the MP3 files and then play them):
http://www.otrrlibrary.org