After a bit of this, I did the usual power cycling of the router, and thought all was fixed.
It's not - it's doing it again/still. Broadband light on the old standard PN-issue Thomson router shows red, indicating there's definitely a problem, but it goes green again while I'm looking, so it's happening just long enough to disconnect me, but not long enough to properly diagnose.
I've spent a long time on the phone today, with no apparent problems, so I don't think it's a voice issue.
Can't find anything at PN (or here) about known local issues - except one guy who's having difficulty accessing his Cheltenham router remotely from overseas - but Cheltenham isn't exactly Bristol, and it sounds as if he's got a much less straightforward set-up, and therefore more things that could go wrong, so I think that one's probably a red herring.
Of course, I've left it (just) too late to call PN, because as it went a while without doing it, I stupidly assumed it was fixed...
Edit: it hasn't done it again since the original post. Dare I hope that it's fixed now, and had absolutely nothing to do with my kit?
Edited by TLM (Sat 12-Nov-16 20:03:49)