The modem came yesterday, and our current connection went dead this morning. At lunchtime I installed and configured the modem, which involved a 20 minute tech support phone call, and now it works.
The phone call was actually rather better than I hoped, as my problem was solved comparatively quickly. It looks as though I just got the netmask on the external connection wrong. I don’t yet know anything about wireless networking, but I was surprised to see that it was enabled and unencrypted by default.
Anyway, we’re now synched to the outside world at 15 Mbps down and 1 Mbps up. Yay!