The British museum was set up to preserve artifacts which would have been looted or destroyed,

This is fairly disingenuous. If the sole purpose was to preserve artifacts, then they would be happy to return said artifacts to original owners once shown they can appropriately store and maintain them.
That is clearly not the case. I think your definition of "legally purchased" may be a little creative. Sure they may have paid money through a trader.. but there definitely was not due diligence, it's basically an old cash converters.