All the configuration appeared to be correct i.e. it hadn't been reset/lost - it's a BT connection so ADSL username and password don't matter anyway.
Eventually, I plugged in a BT Homehub which worked perfectly and proved the link to be fine. I then tried factory resetting the 7800N and the modem came back to life.
The router has been restarted a number of times in the past bit without problem. It's a bit worrying that the modem works without problem for weeks and then randomly stops for no perceivable reason. If it does it again, it will be going in the bin.
