This is crazy but it works. I had been trawling through Google, looking at (other) Apple discussion forums, and getting nowhere. I was about to give up when I came across uniquebobc's post (thanks!). Having followed the various guides, including resetting SMC and other exotica, I can't believe the solution was as simple as pairing the keyboard, then pressing the power/discoverable button on the keypad firmly for several seconds (in the manner of a hard reset), then hitting the large key that isn't actually marked 'Enter' but is in the place that the Enter key usually occupies. It worked straight off. I am dumbfounded but still really, really upset with Belkin's poor after sales service. They've lost a good cutsomer here.