Can a broadband connection be shared in a home?

I think the scarcity or absence of any such solution is because it’s cheaper just to build in a modem than it is to implement the USB protocol to talk to one.

Chuck the old modem in the bin (or sell it for a couple of quid on eBay) and get a 40 quid router modem - you won’t be sorry.

Mangetout is right. The Speedtouch modem is cheap (i.e. given away) because it’s dumb - it relies on firmware being uploaded as the computer boots up. Getting a router to do this would be far more effort than it’s worth.