Balanced audio cables for the win
Faced with this grimy electrical interference noise there was no other option. A trip to my local music shop yielded nothing, so I went up to the hub of all music technology in central London and snaffled the last two cables they had. Being stereo 6.35mm jack to stereo 6.35mm jack. And the grime is gone. Wahey for balanced audio and its magic of noise cancellation.
S => (S,-S) => (S+N,-S+N) => (S+N)-(-S+N) => (S+S)+(N-N) => S