Looks like a typical Ayres set. F.H Ayres was a London-based British toy manufacturer who produced mid-range Staunton sets from late 19th century to WW2. Do the King-sde rook/knights have crown marks?
The only thing that looks like a slight variation to standard Ayres sets are the queen's coronet (too pointy) and the fact that the pieces are missing the tiny third top collar...
And yes, sets can be restored. Not sure what the issue w/ your black pieces is, as the second photo isn't showing, but you can have the set restored professsionally by Alan Dewey (who post here occasionally, and who can be found at chessspy.com)
This set belonged to my great-great uncle who lived in England. I know that he and my grandfather played chess with it during the war, so it's definitely from before 1945. Other than that, I don't know much about it and I'd like to know more. Any help would be appreciated.
Here is one of the black pieces. They are all flaking pretty bad - is there any way to prevent this from getting worse or to restore it?