1) What load is on the power cables in question
2) How good the quality of your other cables are
The general recommendation would be to run the seperately, and you certainly should not run video / audio cables in the same trunking as high current cables such as your ring main.
It's all about the induced current - running a single cable to a projector which is drawing less than 200W should't induce anything into nearby cables. Running a cable alongside a feed for an 8000W electric shower will!
I run mine altogether and have no problem at all but avoid cables which are not well shielded...the more expensive usually the better shielded they are. Try it out first and if it doesnt work then isolate the cables with 2 or more plastic cable channels from B+q or another store.