Dedicated circuit. Ok with its cable alongside/touching housedhold cable??

I'm having a radial installed soon. I want to make use of  a cable channel already running to an existing wall socket that's already in a suitable place near the hifi. The cable for this household circuit section runs to the wall socket from my fusebox though I don't know exactly what route but obviously at the end it's behind the wall's plaster. When the electrician comes he'll trace its route.

I'd much prefer to use this channel for the new radial. If advisable and if possible with the channel also continuing to run the existing household supply in a separate cable to a socket next to the proposed new one (for the tv) .

I think the main deal is the new dedicated path has low impedance and I understand that's a good thing! Does it really matter if on their route the two cables run alongside often touching? (in fact the new one may have two sepatately insulated wires (one a bi-wire)  or perhaps even thee seprtately insulated wires runs (and a similar number, I guess, for the existing wire).