The problem is the varnish, Moody. You need something which won't abrade the surface. You could try using bicarbonate of soda - if the damage is just water marks (from rain or such) then it should work well, If the marks are, as is often the case, resulting from tea and coffee cups, the heat tends to create more lasting damage...where you have to remove the very topmost layer of varnish. Always best to try the least invasive methods first...and if it is just the white residues left from water damage, it is much easier to remedy.