The phone call to Pipex at least established that I'd been looking at the right things but left me with the recommendation that I borrow another router and try it before we got BT involved (as they'd charge me £150 if the issue was with my hardware).

Sorry the troubleshooting continued. I took the existing hardware downstairs and plugged it into the original phone socket that I had been using. It still dropped out, but noticeably less over the next few days. Of course, this could just be Pipex fixing its issues. I decided to get a new router (another Netgear, the DG834G) and upgrade the wireless base-station to 54Mbs at the same time. This arrived today, and I've installed it and it is working like a dream!

Interesting points which I haven't resolved:

1. The service has got more reliable as the week progressed, which could be at Pipex's end.
2. I installed the 3rd and final DSL filter replacement this afternoon, a nightmare job as I needed to take the fitted furnishings in our bedroom apart to get to the telephone socket.
3. The new router wouldn't talk to the internet from the socket which is in the study. It was fine downstairs.

I'm thinking I probably have an issue on the new study telephone extension combined with a glitch at the ISP end. However, I'll never really know.