Hi, thanks for responding.
I was about to upload the thing, and then got to thinking about what you'd do with it if I did - you'd install it, test it, and it might work, or not. That made me think about what would be different between you and me - namely, your location.
So, on a whim, I changed the location code to a different one, and the problem immediately went away.
Looks like it's the data for my particular city that's the issue. Hopefully it might fix itself given time, or if all else fails I can pick a nearby location, which is better than nothing, although it'll mean updating the fifty or so places I've installed this gadget, which I had to do already for the last fix :-( . Either way, at least I now know the cause.
As a final test, I just downloaded a random weather gadget from DeviantArt and tried it, works fine for Berlin, but stops working for Bristol.
Maybe the people in charge of Bristol Weather have all fallen asleep.
Thanks for the offer of help, anyway.