Thanks very much to David and Bruce for your replies.
@ David: the modem is a Belkin ADSL2+ modem, which I believe is
available only here in Australia. It was supplied to me by my ISP. (I
took the path of least resistance on that!)
@ Bruce: your reply prompted me to look at the fine manual that came
with the modem. There's a section in it called "Setting MAC address
filtering" which seems to allow me to do the sort of thing you're
suggesting. I really should've looked there first, shouldn't I?
An Australian lawyer's tumblelog about things (some legal, most not) you
might otherwise have missed