Thanks for all your help, JimmyJ, rv and gtrguy.
Looking under the bridge pickup, the black twin cable does indeed head down in the direction of the bridge so, as suggested, it does appear to be a retrofitted attempt at earthing using a random cable. I have taped over the exposed copper on the loose wire for now.
I worked all the pots and switches and the noises (which sounded a bit different today) have almost all gone away. For a while there was still a little hum that was attenuated if I touched the metal surround of the input jack but that has stopped now. I also had a couple of bursts of crackling but after playing for a while that seems to be gone too. I'll see how it goes over the next few days but the results seem promising so far!
One other data point: while the noises were present they didn't appear to be affected by the position of any of the pots or switches.
Thanks,
Rick.