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There are 3 layers of plaster (brown, white, pink), then paint and then some white glue/sealant on top which is what pulled the layers off when I removed (smashed) the mirror that was previously there.
I was planning to scrape off the remaining sealant (top left), remove any loose pieces and the top pink plaster ‘islands’ in the middle, then have a go with that ready mix plaster @andos suggested. Turns out I have a big square trowel I’d forgotten about.
It doesn’t need to be perfect as we’ll put another mirror in afterwards but probably not a round one so I can’t just ignore it!
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Try to get a blade underneath the white mirror adhesive and slice it off, then clean it with spirits or whatever takes it off (I would start with everbuild wonder wipes). If you've done all that quite carefully you should end up with a paintable surface.
First choice from my toolbox would be a 6" t bar scraper.
https://www.screwfix.com/p/no-nonsense-long-handled-scraper-6/87299
Bit late to the game with this but it's hard to tell from the picture if the white stuff is stuck on the plaster.
If the white stuff is some type of plater that's been used to stick something in place then use a very sharp blade to scrape it off as carefully as possible and use some toupret TX110 to fill any damage to the surface.
Scraper blades are great for this job but they need to be honed through use or by hand to work really well. There are cheap packets of scraper and filler blades available, often called euro style :-
https://www.screwfix.com/p/harris-continental-filling-knives-3-piece-set/41601?kpid=41601&ds_kid=92700047154135765&ds_rl=1243321&ds_rl=1241687&ds_rl=1245250&ds_rl=1245250&gclid=Cj0KCQiA_rfvBRCPARIsANlV66OPONhAypMrmf63Oyd6HSFhF7-MaN6Rn-VAzcpPbl8iIAdpwSsSBcsaAs0LEALw_wcB&gclsrc=aw.ds
The scraper ones normally have a different colour handle and are slightly stiffer.
You're right that a load of kit would make this job easier but you should be able to manage it with some simple ones. It's one of those jobs where you try a few different tools to see what works best.