Many thanks. Can't remove a socket however.
I still don't really know why broadband was down for 2-3 weeks, almost from the day I signed up for it, then suddenly started up 3 days ago and has been chugging on ever since!
Anyway, I'm not complaining; even slow broadband is bliss after Onetel's snail-like dial-up, which seemed to be getting ever slower.
Again, thanks again to all you guys and to this excellent site!

Finally got around to disconnecting the bell wire, as per your suggestion. Result: immediate increase in sync speed from roughly 350k to 600k (no detailed stats yet as the line went down just afterwards!)
Problem: one oldish phone (maybe 15 years old) no longer rings. It's connected through a microfilter, but it was a cheap microfilter -- could that be the problem? I'd rather not bin the phone!
Though broadband now works, it goes down rather too often and can take a few hours to come back. Would a suspect central heating room thermostat be enough to cause the line to go down?
Many thanks

microfilters should regenerate the ring signal, there are some bad designs that don't (and don't filter the ring wire either) so I would change that for a better one.

Many thanks, Phil. After some online research, I see that even supposedly good microfilters aren't necessarily much more expensive.
This is rapidly turning into a crash course in telecommunications for me, for which I'm grateful to you guys.

Final postscript to all the above, I hope.
It's clear now that all the initial problems, plus later ones of ADSL going down sometimes for several hours at a time, were due to that bell wire. Strange the ISP people never mentioned it. Speeds now regularly above the promised 512K.Thanks to RobertoS.
A better quality microfilter installed for £3.50: old phones ringing their heads off now, and for all I know it contributed to the stability of the line. Thanks, Phil.