The Greeks did not become that interested in their sculptural history until within the last century. The pictured image "Athena of Piraeus" was discovered when digging a sewer line. It had been buried as junk. It's been over thirty years since I took the class, but IIRC, a museum director was walking by and saw part of the arm as a backhoe operator opened the hole. When the director tried to stop the project to recover the sculpture, the workmen became very upset and threatened him. They feared the job would be shut down for an archeological dig.
That is true of the Turks who occupied Greece for 400 plus years. Turks have not changed BTW although they are trying a new strategy these days...
Worst damage? The Parthenon was bombed to smithereens when a Venetian bomb (1687) fell in it exploding the ammo dump it was under the turks. Turks stored their ammo right in the middle of the temple.
Following their independence from Muslim slavery the Greeks as a whole did more than humanly possible to protect their patrimony so much of which was destroyed and damaged and sold during their enslavement. No - the British did nothing to preserve these marvels—in fact, their attitude today speaks volumes about their guilt.
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Much of the art of Classical and Hellenistic Greece was destroyed by the Greeks themselves as pagan when they converted to Christianity. Sad but true.
The british scraped teh paint and bleached the marbles.
Duveen made molds which further deteriorated the marbles. (each mold he pulled created further damage)
The british museum aristocrats were far more abusive than any weather.