Thought I'd pop back for a postscript...
It's fixed. Turned out it was the pedal after all. Re-greased them yesterday and now all is fine.
In case it's of interest....I discovered in the course of my flounderings that pedals 'should be regreased every 2,000 miles or so', which came as news to me. I'd always assumed they just went on for ever. I suppose I've probably done about 10,000 on these from new, so they did pretty well. I also discovered when I got round to taking them apart that I think the problem was partly self-inflicted, in that when I first suspected possible pedal problems, I dribbled prolink gold into the bearings as best I could. When I got them apart, I discovered that one set of bearings was indeed now full of prolink, which seemed to have dissolved and washed out whatever grease was in there, leaving behind lots of lubricant, but stuff that was too light and thin for the task in hand.
I guess I'd draw two conclusions from this whole episode: exhaust all (relatively easy) possibilities before doing anything really major (I was on the point of stripping out the BB, which I think would have been a mistake, as well as a complete waste of time & effort); and prolink doesn't, after all, solve everything.
Thanks for all advice. Good luck with all your ticks!