Hard disk failure. The nice people at Bytemark got a new hard disk installed within a couple of hours, and I had practically everything backed-up, but the restore process turned out to be harder than I expected.
In particular I’ll mention (because it was the only one I couldn’t solve on my own – wordpress authors don’t seem to be logging error messages for catastrophic WordPress failures, I’m not sure why!) – WordPress displayed a blank page for every URL because if WordPress can’t find the theme it thinks it’s using, it silently – no errors, no messages, no hints – just displays blank pages everywhere. Not even any HTML. And I had forgotten I was using a custom theme that I hadn’t restored :) – doh!.
Also, for some reason the last 3 weeks of posts are missing. I was sure I had a backup from last week that should have had them, so I will continue to investigate.