Fascinating discussion, but if I may go back to the original issue.
Regarding my original Q, it looks like it's only me (thanks for the input) so I'll need to investigate further. I'll try some battery voltage checks and taking the car for a really long run to charge it fully.
So today I dug out my multimeter, which (at various times) gave voltages across the battery between 12.5 and 12.7 with the engine stopped and 14.25 with the engine running. Ambient temperature throughout was between 2 & 3 degrees. That all sounds fine to me, so the battery itself and the charging system seem OK (?)
I've also done a run totalling 80 miles: 40 each way, with a pause in the middle to check voltages and give the car a chance to start anew as per John Ratsey's suggestion: idle-stop didn't function at any time. The multi-display messages varied, sometimes it was just the circled-A-with-a-line-through-it, sometimes it had the low battery indication as well. At the end of the run I got the "low battery" indication, but yet measured the battery voltage at 12.7V.
Called my local dealer, who immediately knew what I was talking about because they've seen it before and have had to "reset the system" (whatever that means) on other cars. So I'm booked in for that ... although not until 1st March because (apparently) they are "snowed under with airbag recall work".