I'll add my own links, if I may, Ann:
RadioEchoes is temporarily down but I'll provide the link anyway (in the hope that they can sort their problems out soon):
http://www.radioechoes.com/
It's a vast repository of old radio programmes. They're mainly American but there are hundreds of editions of The Navy Lark, The Men from the Ministry, etc on there as well. You can choose between streaming them directly to your computer or downloading them as MP3 files.
Abacus British Comedy Radio broadcasts 24-hourt non-stop classic British radio programmes, such as The Navy Lark, The Men from the Ministry, Round the Horne, Hancock's Half Hour, The Clitheroe Kid, etc, as well as some newer content, such as Cabin Pressure and The Castle. They don't publish their schedule but regular listeners soon get to know when certain programmes are likely to appear:
http://www.abacus.fm/british-comedy.html
ROK Radio's British Comedy Channel 1 has similar content but from a more diverse range of programming
http://rokradio.com/program-schedule-british-comedy-channel/
as does their British Comedy Channel 2
http://rokradio.com/british-comedy-radio/
ROK Radio's Old Time Gold Channel has a mixture of British and US content, with both drama and comedy:
http://rokradio.com/program-schedule-old-time-gold/
Goon Show fans can find continuous broadcasts both here
http://www.abacus.fm/goonshow.html
and here
http://goons.fabcat.org/
The Old Time Radio Researchers' Group has a library of downloadable programmes, in MP3 format. They're mainly American but there is some British content included:
http://www.otrrlibrary.org/