Thanks for all of the replies, guys!
I've taken your advice, removed the wheel and wiggled the pads around in the caliper until I could see their condition. And it seems that there's still about a millimetre of material on each pad.
I've also done a bit of snooping around on the net, and it seems that the replacement pads aren't too difficult to get hold of. Here's one example, although a bit more research will tell me if this price is competitive...
http://www.tredz.co.uk/.Avid-BB5-Organi ... _33384.htm
EDIT: I've checked eBay, and there is a big price variation for Avid bb5 pads, from about £5 to about £15...
1993 Saracen Sahara Elite (with a few mods...)