Having discovered that Adobe AIR only supports debian/rpm based systems (which mine isn't) and downloaded the SDK instead (as per the recommendations in the Adobe forums) and upgraded to Flash 10 (as BBC wouldn't let me download otherwise), I discovered that the iplayer desktop still wouldn't download. Not sure if it's a bug in Flash 10 (which sounds buggy according to google) or in the flash on the bbc site, but I don't seem to be able to press the buttons in the flash image to get it to do anything. I wonder if anyone else has had any success with it.
getiplayer on the otherhand, I just downloaded and popped in /usr/bin and it does exactly what I wanted (i.e. lets me watched downloaded programmes from iplayer rather than just streamed ones).
Might try the iplayer desktop again later, but I'm set up to do what I wanted to for now.