Not suggesting you take up any tarmac Nick, simply suggesting you try running a piece of wire to the best/cleanest ground in your house, the water pipe where you can see it come into your home, it's usually exposed where you can see it in the utility closet? next to the boiler? There might already be a ground cable on it being used for something else, there is in my house ..every home is different. In my home this would be a quick and easy to try experiment, it would only take me 15 min., but if it's a project for you I can understand.
4 core interconnect used throughout everyone's Naim system is similar too and never seems to be an issue. Naim commonly seems to use the shield/ground wrapped around the yellow wire -for consistency I suppose- and then sometimes the yellow core isn't even used for one of the R/L signal channels -not consistent-, only it's shield is used soldered to the connectors ground Din pins on both ends of the cable, the 3 other copper wrapped internal wires simply touching each other whether for stereo or if all 4 being used for tape in/out.