Praise be!!! The problem is now sorted and, yes, btorz it was apparently a fuse that had blown. To be honest, that had occurred to me, too, as a possible cause but as the car was already booked into my local garage anyway today (being treated for another minor and - we think - unrelated problem with the driver's electric seat motor) I let the auto-electrician check out that aspect of it, and it turned out to be the cause.
Thing is, I couldn't seem to find out myself which of the many fuses was responsible for this particular feature on the car, and to be honest I didn't fancy standing outside for any length of time in this freezing weather checking each of the fuses in turn looking for a blown one.
Anyway, all's well that ends well, as they say, and thanks to both of you for your thoughtful contributions. Now if I could just find someone who can tell me where to get hold of a couple of central-locking motors for my two passenger doors...