So you will have these three zone costs for each product? If so then you should first add the three zone columns to your cart. Next you would need to edit your add to cart server behavior to include the zone shipping prices for each item.
Once you have it setup like this you will need to determine the zone the user is shipping to. To do this you can check on the session variable that holds the shipping country. Based on the shipping country you will determine which zone to use. For example, the first shipping charge rule will check to see if the country is UK, if it is then you will use the subtotal of the zone 1 column for the charge amount. The next rule would check to see if the value of the country is USA or Canada, if so then you would use the subtotal of zone 3 for the charge. Finally you would just check to make sure that the shipping country is not UK, USA, or Canada. If it falls into this rule then it would use the zone 2 shipping charge.
Please post back with any questions that you have about any part of this and we will help you with what we can.