Remove protruding brick on LR chimney

The brickwork on a chimney breast of a 1900s house will be solid brick (not veneer).

Cutting a channel, fitting trunking and replastering is eminently sensible if that's the only way to go. It's also a job you can do your self with a masonry drill and cold chisel. Using an SDS drill with a chisel attachment will be quicker if messier.

Make sure you take the cable vertically (if possible) never diagonally across the wall. This will make it safer for future owners of your house.

The "traditional" way to do it is, as you have suggested, to cut the bricks out by hand (and refit the cut bricks once you've done to give a tidy edge). It can be a time consuming job.

The more usual way to do it once the lintels are in place would be to use a disc cutter - usually a petrol driven one - (aka a rotary cutter or Stihl saw, after the common brand) with a diamond-tipped blade to cut through the bricks. This will make a lot of dust. You can get a water pack to reduce the dust (and cool the disc, reducing the wear on it), but it can still make for a messy operation, as the water will make the dust into a slurry that the disc will spray about.

You can hire the saws from pretty much any plant hire outlet, who will also hire the diamond tipped blades, charging you per milimetre (or half milimetre) of wear. That can be expensive though, so if you've a lot to do, it might be cheaper to buy the diamond-tipped disc from an independant supplier.

I've also seen what is basically a chainsaw with a diamond tipped chain for cutting through walls, etc, but I've not actually seen one used to comment as to how effective they are.

Don't forget that you should use eye, ear, and dust protection if you're doing work like this.