I still don't know exactly what has caused the keyboard problems that I've encountered with my Pi, but only yesterday I finally managed to find one in the house that works with no issues at all...
I tried three USB keyboards. The first was an A.N.Other-brand wireless "media centre" keyboard/trackball from Maplin (which I "borrowed" from another PC of ours), which was constantly repeating keypresses and was basically useless for the Pi (but OK on other machines). The second was a cheap no-name wired USB keyboard, which caused the Pi to kernel-panic every time, the moment I plugged it in.
Third time lucky? Well, yes - a Dell wired keyboard worked fine, but (a) I really wanted wireless (the Pi is using our TV as a display), and (b) the keyboard was borrowed and I had to return it
So, what else could I try?
The answer had been staring me in the face the whole time: the Logitech K360 USB wireless keyboard we use (occasionally) with our Wii! I plugged the nano-receiver into the Pi... and the keyboard worked perfectly as long as the Pi was switched on.
Now, the original wireless keyboard/trackball is plugged into the Wii, the old PC has the "no-name" wired k/b, and the Pi has the K360.
What a "palaver" - I'm just glad I didn't have to buy another keyboard, which might not have worked either... all is well now