Just to round this thread off, I'm now back at my flat, but the battery I ordered is sitting at a pick up point in the next village because the carrier was unable to deliver it here. (I find that quite difficult to believe as there's always someone around in one or other of the flats and we all take each others parcels in, but no specific reason is given on the card they left, so perhaps only my signature will do in this instance.)
Much more in hope than expectation, I checked the battery that was still working 2 years ago and unbelievably (to me at any rate), it showed it was still fully loaded! I've now brought one of the bikes up from the cellar, pumped up the tires, put the battery in place and hey presto, off I went down the road, everything working as normal.
The temperature is forecast to be 34C tomorrow, so walking in full sun for an hour or even cycling all but the shortest distances isn't something I'd relish doing. Luckily I have very friendly neighbours, one of whom has said she'll drive me down to collect the new battery tomorrow afternoon. First thing I'll do is check the + and - signs are the right way round as it's not possible to see from the pictures.
Thanks for your help, if the old battery really is still fine, it's all due to following your advice in earlier threads about how to treat it.