This particular site is using an implementation of PowerStore with the shipping charges altered using the eCart.
The idea here is the same, you will check on the ship to country and store this in a session variable. Then in your shipping charge rules you will have three, one for UK, another for Ireland, and another for North America.
In your shipping charge rule you will check on this session variable to see if it is UK, and also the total of the order. If it fits that criteria then you would apply the flat rate amount you specified in that rule. You will need at least one for each country, and if you have multiple shipping rates to offer then you will need to have that setup for each country also.
You get the ship to country on the pp_confirm page. It is part of the bindings for the PayPal Express Checkout. Please post back with any questions that you have about any part of this.