Found this on another site...
A. A really successful method of cleaning Zinc is using 'Silvo' or 'Brasso'. However, I should warn that this only works if you're looking for a non-weathered look.

Using Silvo Silver Polish [linked by editor to product info on Ebay] you get quite a shine on the finish. People call it a 'mill' finish. It's nothing like polished chrome or anything, but it gives a kind of rustic shiny look which will then tarnish down and become progressively more matte with time and use. Brasso [linked by editor to product info at Amazon] gives much the same result- but I have found that it polishes up slightly more matt/cloudy than with 'Silvo'. So use either depending on what look you want.

For Zinc that has been 'pre-weathered' (blue/pinky/dark grey hue) you're pretty much stuffed... The best thing you can do is the above- with some serious elbow grease! Believe me, I've tried! Will come out great, but is a lot of work. Hope this helps, Luke

What material was the table cloth? It looks like a chemical reaction between the water, the table cloth and the zinc.

Hi what did you end up using to restore it? I have a similar problem and would love some advice on how to restore it