I have a book called 'green clean' filled with all kinds of recipes, and it suggests using vinegar (apparently doesn't leave a film). They say 55ml to 4 litres of water, or put it directly on a sponge for harder to remove dirt.
Another tip is to rub the area to be cleaned with half a lemon dipped on borax, baking soda or salt, rinse well and dry with a soft cloth.
Don't know if they work, but worth a try