From BBC
The BBC "Listen Again" links are of the form http://www.bbc.co.uk/radio/aod/networks/radio1/aod.shtml?radio1/r1blueroom_sun. If you download this file by typing (in Linux) wget -O radio.html "http://www.bbc.co.uk/radio/aod/networks/radio1/aod.shtml?radio1/r1blueroom_sun" and then look inside, you'll find a line of the form
var AudioStream = "/radio/aod/shows/rpms/radio1/r1blueroom_sun";
and then a bit further on there is a line that says
<embed src="'+AudioStream+'.rpm" type="audio/x-pn-realaudio-plugin"
Altogether this means that the filename we're looking for is the base BBC URI + the AudioStream variable + .rpm, or http://www.bbc.co.uk/radio/aod/shows/rpms/radio1/r1blueroom_sun.rpm which is the file that names the file we want to download. So we download it again, and the total contents of the file are
rtsp://rmv8.bbc.net.uk/radio1/r1blueroom_sun.ra
which is a Real Time Streaming Protocol indicator and the thing we actually want to download. We can download it using mplayer, mplayer -dumpfile track.rm -dumpstream rtsp://rmv8.bbc.net.uk/radio1/r1blueroom_sun.ra and you're left with a lovely Real Media file (you can find out exactly what format the file is in by typing file blueroom.ra).
From Oxide Radio
Oxide, Oxford Student Radio, streams their content on the internet via Windows Media Player, iTunes and Real Media. I've found it convenient to use their Real Media format available at http://163.1.67.201:8000/listenLive.m3u, although this file just contains a link to the URI http://163.1.67.201:8000/listenLive.
The recipe is pretty similar: mplayer -dumpstream -dumpfile track.rm http://163.1.67.201:8000/listenLive.
Converting, editing, compressing
The track can be converted to WAV file, which is a high-fidelity format, with the command mplayer track.rm -ao pcm:file=mytrack.wav -vc dummy -vo null. Be aware that the WAV file is likely to be more than 10 times larger than the original Real Media file.
Now would be a good time to edit the file using Audacity - make sure you've only got the stuff you want, and apply effects that may be necessary. Then export to either OGG or MP3 (MP3 requires LAME to be installed) using the techniques described in the Linux Journal: Podcasting for the Penguin. Note that an OGG quality setting of 0 with a sample rate of 22kHz is decent for speech podcasts, and in my experience gives file sizes of about 18MB per hour of speech.