A few years back I used a bit of software called Radio Downloader to listen to things I'd missed. The chap who made it discontinued support for BBC programmes after claiming he was being leaned on by the Beeb who were making noises about copyright infringement. This looks like an excellent replacement. Thanks Guvnor.
I've used this quite a lot in the past. It does the job nicely once you get the hang of how it works. Every now and then the Beeb changes how they index tracks or stream them which breaks it, but the fixes come fast.