Update: I drove up to Middlesbrough and installed the Mac Mini. The cable from the NTL wall box went directly to a splitter feeding the Digital TV decoder and the broadband modem. The cable was white foam-filled (very solid looking foam) coax. However, I noticed that the original Sky dish cable was still there and looked like CT100, in good condition. So I cut it from the dish and routed it directly into the spare bedroom. Connected the bottom end to the splitter and connected the modem upstairs with the short Ethernet cable going to the Mac.
Setting up was easy thanks to the info given here (thanks). Email was a bit tricky to get working until I did a Google search and discovered that Apple "Mail" has to have its SMTP port set to 25 for NTL. Once that was done, everything worked just fine. Mum is now a happy bunny.
In summer I'll go back and install the proper NTL coax but it was brass monkey weather on Saturday and the CT100 seems to work OK.
Oh, an interesting point for Mac users. I wanted to be able to see what was on her screen remotely so I enabled the (Tiger) VNC client (on Mum's Mac Mini 1.25GHz) in
System Preferences -> sharing -> Apple Remote Desktop.
I downloaded and installed "Chicken of the VNC" onto my (Panther) G4/1.4
tower.
When I returned home, I launched "Chicken" and entered Mum's IP address
that I'd thoughtfully emailed to myself.
Chicken connected immediately and I was able to see the Mac Mini's screen
contents, move the mouse and use my keyboard. The only downside is that
each screen refresh takes around half a minute. Hey, but I'm not
complaining!