This was on Windows XP, and the Vista machine didn’t have a problem. The wireless printer had connected through to the wireless LAN, but the XP machine was not detecting the printer and there was no particular error.
It turned out to be the Windows XP firewall that was the problem. When I switched off the firewall the printer connected. In the time I had on-site I couldn’t find how to open the Windows firewall to that specific network, so I installed another firewall instead and left the Windows firewall open.