Yep, the widget takes you to Amazon.com, but when you click on "United Kingdom" almost at the bottom of the page, just under the Amazon logo, you will be transferred to Amazon U.K. and you can start buying there; it might get Jim a commission.
When you put things in your cart on Amazon.com, they will not show up in your Amazon U.K. basket; all Amazons are autonomous in that respect, widget or no widget.