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Thanks all. @dbr 's comment wins - flat is sold, I just need to remove the batten and fill the resulting hole before the end of the week...
The screw is absolutely definitely not moving. I've tried with a power driver, and a manual driver, and I've even tried making noises while I try to turn it. But no luck.
Father in law arrives tomorrow with a reciprocating multitool, so it'll be gone by lunchtime...
Cupcakes-
flat is sold, just need to
cover the whole thing in expanding foam an walk away without looking back
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I would either try and snap the head of the screw with an impact, or drill the head off with a big HSS bit. Then when the batten is off, either hammer what's left beneath the wall level or twist/pull the remnants out with vice grips. Then fill whatever fresh hell has been left behind.
NotThamesWater
stevo_com
Remove entire wall and fill wall shaped hole with whatever Toupret Airhead says
Or sell house