Can You Timeshift Streaming Audio?

Ralph Bearpark asks: "There are several hundred/thousand radio stations out there putting out live streaming audio on the Internet. What if you want to regularly record your favorite show at, say, 11:30 on Wednesday on BBC Radio 4 and then, maybe, download it to your MP3 player for listening on the move ... How'd you do this? Is there software out there already? If not, what would you need to put it together?"