As has been suggested above, I usually back the plasterboard with a piece of ply. I just cut out a decent sized, convenient square between studs, then insert a piece of ply bigger than the hole, held in place with a couple of drywall screws. Then screw the piece of plasterboard onto the ply, tape and skim.
I cannot plaster with traditional British plaster, but have plastered many rooms using the tape and skim method like the Americans and continentals do. It is easy to get a good finish as you can use multiple thin coats and sand between coats. It's much easier than just cutting a slot and with good jointing tape and compound it is easy to get a good finish.
Cut the hole with something like this: Minotaur *** Saw 6"
Cover the cuts with self adhesive fibreglass mesh tape, something like this:
Diall Fibreglass Mesh Tape White 90m x 50mm
then use several coats of something like this:
Knauf Joint Filler Premium - 10kg | Wickes.co.uk
You can use ready mixed, but it tends to be a bit sloppy. When everything is back to how it was, screw your handrail into the ply through the plasterboard.
I am pleased to have learnt a new word today from Garden Shed Projects - patress.
If you really want a good finish you need one of these
, it will drive you insane as well as bankrupt you:
Surface control light STL 450 240V SYSLITE