Well, I think I've solved it.
I was a bit surprised the signal strength was fluctuating so much, so I took the laptop into the office and stood it next to the WiFi. It still dropped the line every few minutes.
After messing with lots of settings (locking the modem/router to 802.11b rather than b and g; changing channels etc) I found a toggle that said "Allow Windows to manage my connections" on the controls for the WiFi card.
I turned that OFF so Windows can't mess with the card, and the line has been up and working with no hiccups for the last 7 hours. Fingers crossed.