UPDATE:

Went to my local friendly telescope shop with the ETX and handbox. Plugged in another handbox - same problem. Scope slews in altitude in both directions but not anticlockwise in azimuth (clockwise slewing is OK). So, it's not the handbox and it's not the curly cable.

Took base of ETX off expecting to find loose/broken wire but none were obvious. A loose plug, but no, that's not the problem either.

So it looks like it is an electronics fault in the base of the ETX, so back to Telescope House it goes!

Steve (at TH) guesses that it is a driver chip on one of the boards inside the base.

Art