Cost to do cable work at LBS?

£80 sound like a mid-level service (silver service) which is an overhaul of your bicycle, assuming you don't want that, even for an overhaul, £80 is way too much.

Brake service only should be £15-20, possibly more if bar tape might need replacing.

Imagine signalling to turn right and attempting to simultaneously using your left hand to control speed, tell me whether you would prefer this left hand to be connected to a rear brake of front?

It doesn't matter one ounce.