Both the Kindle and the Nook provide free 3G service here in the States...basically if the network (either Sprint or AT&T, depending on when you bought your reader) is available, you can get wireless access.
for the UK, you might want to read this-not sure how updated it is:
http://ireaderreview.com/2009/10/07/...uk-review-faq/
For now, accessing the bookstore and the web with a Kindle probably doesn't use much bandwidth-cheap enough for Amazon and B&N to subsidize it thru the price of books and the hardware cost. But if/when they go to full color, more capable readers, I wonder if they can afford to pay for the bandwidth-especially as other 3G data users pay $30-$60/month for the privilege.