the picking up the phone thing suggests a microfilter or SSFP gone bad, or a bad design.
Yes, that was one of the things I suspected the first time this issue occurred. However, since then, I've tried the Mk2, Mk3 and (after Openreach changed the NTE5A to an NTE5C) Mk4 SSFPs as well as the Excelsus Z-350UK plug-in microfilter and whatever the plug-in filter Sky and TalkTalk supply with their routers is. I also had a go with double filtering (specifically the Mk3 SSFP with the Z-350UK plugged into its filtered output and the phone plugged into that), none of which made any difference. I also get the crackling with no microfilter at all and just the phone connected to the test socket, and the random disconnections and SNRM oscillations with no microfilter and just the modem connected to the test socket.
That said, you've just reminded me that I should probably check on the current situation with a different modem, phone and microfilter before Openreach come, just in case it is one of those this time round, so thanks