I bought three webcams matching one I already had, for a total of £16 off eBay.
The good new is they all work.
The bad news is that they can't all work at the same time, as they saturate the entire USB bandwidth.
I now know that cheap webcams send a raw stream of video frames over the wire, whereas more expensive ones compress it (with mjpeg or similar) before sending it over the wire. I now also need to buy more webcams - but more expensive ones.