Thanks for an illuminating set of replies, folks.
A couple of points. As I said, we were at FL380, and the OAT was quite cold, at about -65ºC. We were somewhere near 4 hours into an 8-hour flight (there was a favourable jetstream: the schedule was 10hrs 15mins, and we arrived in about 8hrs 20mins flying time)
The water came through on both sides of the ac at the same time - so presumably not stuff leaking in bins (intentional or otherwise).
Looking at a cutaway diagram, these seats were almost exactly below the upper galley. So a leak/blockage there may well be the cause. If that was the case, the cabin crew's reaction seems even more cavalier than I thought, since the liquid might well have been something other than clean water.
easyflyer
It sounds like you don't particularly like crew if i'm being honest.
Not so, I have absolutely no problem with CC in general - just these particular ones and their lack of care for their pax.
spannersatcx
Just because there is no in seat IFE doesn't mean the a/c is old.
I accept that in general, but I've been flying United between SFO and LHR, and various places in between, for about 20 years, and I can't remember the last time I saw a long-haul ac without in-seat IFE. So I reckon, with other clues as well, that this was a fairly long in the tooth ac.
Anyway, thanks again for all the suggestions.