The BBC do offer you the chance to listen to all sorts of shows again on your computer.
Go to this web site
http://www.bbc.co.uk/radio/
On the right it says "Listen by Genre".
Select "Music" and there are all sorts of sections.
For example one of them is "Easy and Soundtracks"
If you select this you get about 50 different shows of easy listening music covering the 20's, 30's, 40's, 50s and 60s, musicals, films, and so on.
As an example one of them is called "Vintage Vinyl" which says "All the best songs from the 1940s through to the 1970s"
There are a limited number of stations the BBC can have, but I do think they provide excellent coverage on the interent.