This is a picture of soon to be step- daughter's new table, a very good make here in the US made around 1979 and due to humidity and temperature variations this brickwork like crazing is showing itself in patches, this is a known problem over here, done a bit of research which suggests that after removing all dirt grime and possible silicone it should be lightly sanded until the top of the stain is reached and then re-bodied up using shellac/French polish.
My thought is that after a clean and a light rubbing with some 0000 steel wool, I go over it over with a rubber that will fill in the cracks maybe even melting and blending with the original surface.
Then a thin layer all over the table, as you can imagine I am very loath to sand most of the surface away!
Any thoughts, ( my first thought was to run a mile) Ian