The BBC's digital "Comedy and Drama" channel, BBC 7, runs Round the Horne and an earlier program with many of the same cast, Beyond Our Ken, every week. It's available online as a streaming audio service:

http://www.bbc.co.uk/bbc7/

The same channel also carries many other old BBC comedies, including The Goon Show, Tony Hancock, I'm Sorry I'll Read That Again and lots more.