Is that fire (and godawful fireplace) in use? You probably don’t want a TV directly over the top of it if so. If not then knocking out a brick to access the cavity behind will get you to floor level though I’d be tempted to chase a conduit horizontally to where the shelves are. And by that I mean, I’d be tempted to get someone else to do it for me, I’m quite practical but I do have my confidence limits.
Where are these cables going to? One of the plug sockets in the corners? What else? Aerial for terrestrial TV, sound bar, games console… ?
I had this issue recently. I got a TV almost as wide as the chimney breast, painted the wall a dark colour and used a couple of lengths of this stuff.