OK - stuff I've now tested:
Connected power and earth directly to the headlamp socket - HID firews up as expected, so its definitely a power supply problem.
Disconnected the only Autoswitch connection I made before noticing the failure (purple Autoswitch wire to the 'Power On' connection of the BMW fog lamp loom) - this had no effect (as expected).
I'm a bit flummoxed as to what to do next. The problem doesnt seem to be in any of the areas I have done work and the light was working perfectly a week or so ago when Peter & I fitted it. The two cables disappear into the loom ahead of the headstock...
Anybody got any ideas?