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Hold the baton in place level and drill through it with a wood drill bit just enough to mark the hole. Drill the hole with a masonry bit
Yep, would agree with this - make sure the wood drill bit is smaller than the diameter of the screws you're using otherwise there'll be no material left for the screws' threads to pull on.
hammer the screw in a rawlplug through the batten into the hole
I wouldn't do this, as it'll make an unnecessarily large hole in the wooden batten, which could lead to loosening/failure.
Use a masonry drill bit of the correct size for the rawlplug, with the batten out of the way, and then put a screw through the batten into the waiting rawlplug. If you put a rawlplug in and it's protruding slightly, you can just use a chisel, or maybe a Stanley knife, to take off the protruding mm so that the batten sits flush against the wall. Trying to remove rawlplugs is a recipe for crumbling walls and enlarging holes too far.
Hold the baton in place level and drill through it with a wood drill bit just enough to mark the hole. Drill the hole with a masonry bit and hammer the screw in a rawlplug through the batten into the hole. This has worked for me for skirting - but obviously skirting is less susceptible to moving.
I got some Dewalt bits from Toolstation that aren't round at the chuck so don't spin and they've worked really well.