Wow! Thanks everyone for the replies, and of course for the answer.
It occurred to me the fan could make some mechanical noise that disturbed our mains circuit,
and next check was to run guitar amps with ceiling fans on and off. I didn't quite get to it.
Next, I considered it might be to do with correction of our 50Hz mains frequency where it might still be used for timing.
Now that I know the answer, to maintain intellectual honesty, I can't complain about the noise too much!!
"To be honest, not knowing it's origin is more annoying than the actual interference. It doesn't overpower anything."