Well, to give credit where credit is due, after exchanging some further information with UKOnline_Dan, he arranged a BT Health Check on my line, and it happened today.
In the meantime my connection had deteriorated to 800 kbps down / 1024 kbps up, SNRMs 4.7 dB down / 6.0 dB up, attenuations 55.0 dB down / 31.5 dB up (from initial 2593 kbps down / 728 kbps up, SNRMs 6.5 dB down / 9.5 dB up at much the same attenuations, 54.5 dB down / 33.0 dB up, see
http://bbs.adslguide.org.uk/showthreaded.php?Cat=&Board=technical&Number=3500487&page=0&view=expanded&sb=5&o=0&fpart=).
It transpired that the Openreach engineer had, all in all, 2 hours for the Health Check, and some of this time had been already spent at the exchange, at the green street cabinet, and some further time went into checking an extension, despite my polite attempts to convince him to focus his attention on the situation at the test socket. At the test socket, the engineer's USB modem connected at 1024 kbps down / 1024 kpbs up, and we observed the expected rapid accumulation of CRC errors.
The engineer's next step was to disassemble the grey box outside the house, and disconnect and reconnect the underground cable to the in-house wiring. The unexpected effect was that after he did that, his USB modem could no longer establish a connection. However, a brand new Netgear DGN2000, which had arrived on the day before, managed to sync at over 2800 kbps down / 1024 kbps up. At this moment, the engineer decided to check the connection rates at the street cabinet and some time thereafter called me to report that at the cabinet his USB modem could sync at 7768 kbps down / 1024 kbps up and attenuations of 44 dB down / 26 dB up, and there were no errors whatsoever. This was very much at the end of the 2 hours allotted to the Health Check and, in effect, the engineer left without returning to my house, and without being able to prove connection through his equipment at the master socket.
After some experimentation with the three modems that I have at the moment, a Netgear DG834Gv2, a Speedtouch 585v6, and a brand new Netgear DGN2000 (all with the latest firmwares), it became obvious that the Netgear DG834Gv2, which had been capable of maintaining a reasonable connection until a fortnight ago, was no longer able to do so, similarly to the engineer’s USB modem. The Speedtouch 585v6 managed to achieve for some time 2816 kbps down / 992 kbps up at SNRMs of 5.0 dB down / 6.0 dB up and attenuations 54.0 dB down / 31.5 dB up, but CRC errors started to accumulate once again towards the evening, with the expected detrimental effect on throughput (the thinkbroadband downstream speedtest results deteriorated to 570 kbps from 1496 kbps earlier in the day). At the moment, I am using the Netgear DGN2000, which is achieving 2266 kbps down / 762 kbps up at SNRMs of 4.9 dB down and 9.0 dB up and attenuations of 55.0 dB down / 32.3 dB up with reasonable CRC counts (due to an ADSL2 connection making use of SRA).
So, all in all, the BT Health Check brought about some improvement and showed that my line had been suffering from two different faults: bad connections within the outside grey box, and something else, potentially more substantial, along the underground cable from my house to the street cabinet, which is still there. A trace of the route of the cable on Google maps shows that it is just under 1 km long which is perhaps a bit too long. There are new marks (distances and arrows) on some of the covers of the inspection chambers which suggest recent work which may have changed the condition of the line.
To conclude, after the BT Health Check, I have a line which for the moment is working better, but only with some of my equipment, and not with the equipment of the Openreach engineer. I would welcome ideas as to how to proceed in this situation, and hope that UKOnline_Dan will be able to extend his support until the problem gets fully resolved.