Fishing Multiple Cables through Studs

[CElwell]

Afternoon all!
I have what I think should be quite a common issue but can't seem to get my head round yet!
For hidden cabling to a TV mount, I'd like to run 4 cables (a power cable, two HDMIs & one SCART) from the mount to a cabinet set (currently another project).
So first problem, I know that consumer power cables should not be run inside walls - I've come across apparently a legal product called syncbox which claims to get around this, I assume is only legal if you literally spur off the existing socket to the syncbox mount with 27A,T+E? If that's the case, what's the procedure for running the other data cables can they all be banded together behind the wall and through stud penetrations together etc?
Brings me onto second problem, I want to run the cables down approx 4ft, and across approx 4ft, so will obviously come across a vertical stud at some point to route the cables through. Given this number of cables and that I can't work out how I would get all of them through the same hole using a flexi bit, and don't really want to be making big cuts in my wall, I was thinking my best option would be to remove the skirting, take the cables down a bit lower with a magnapull then hole saw through the stud at the bottom, does this sound ok?
Appreciate any help..

 

[telectrix]

cables must be run within prescribed zones. basically that up/down/left/right, in line with sockets or switches. the exception is within 6" of the ceiling or within 6" of a corner of 2 walls. also, your signal cables should not run with mains cables. best advice is to get an electrician to install this for you.

 

[CElwell]

cables must be run within prescribed zones. basically that up/down/left/right, in line with sockets or switches. the exception is within 6" of the ceiling or within 6" of a corner of 2 walls. also, your signal cables should not run with mains cables. best advice is to get an electrician to install this for you.

Thanks for the prompt reply telectrix!
Having done a bit more research now I can see the issue :/ if I were to pull the cables directly up the wall into the loft then across and back down vertically that wouldn’t be a violation then? And gets around the stud issue, but does seem like a waste of cable for a short distance! Final question, with power and data separation I’m seeing 50mm getting banded about a lot with separating power and shielded hdmi, but nothing really specific. Do people just do the cables in separate runs (ie not the same conduit) and hope they don’t get too close inside the wall?