Thanks again for all your replies, and to freeola for the extra info.
Just thought I should give an update after a (friendly) engineer came yesterday ...
He checked the exchange on the way, which showed an ADSL signal was present on the line.
On arrival, and a few questions, he said he would look at some of the cabling on the outside of the house 'which didn't look right' - the previous owner had had two lines which they had later had changed to one line and an extension.
Apparently, part of the cabling looked like it was 'looping back on itself', and he just re-routed the cable that was there so it went directly into the master socket and back out.
After this was done, and a new Openreach-branded master socket fitted, a router was plugged in, and it was able to detect a ADSL signal and sync. He then carried out many tests which showed the line to be fully operational.
I asked what had caused the fault, and he said he wasn't sure... so I guess I'll have to just wait to see if there's any charge to pay.