Then I realised something. I'd always assumed the mantelpiece was some sort of strong wood. But for the first time ever I could see the underlying material, which turns out to be translucent white stone which I'm pretty sure is marble.
So, my tentative long term plans for renovating the flat have now expanded to include "get a big can of paint stripper and find out what the rest of this is like." Just hoping that it doesn't turn out the paint is covering damage - can't see any signs of it, but since the paint layers are about 3mm thick they could be hiding all sorts of surprises.