Since there is a relative who lives in the states, why can't they just get a credit card with UK person's name and USA person's address. UK person can pay the bill. UK person then downloads books through computer and USB, rather than wirelessly.
I'm not sure how to do that last, since I have a whispernet connection, but amazon's FAQ pages say it can be done. quote:
If you have a computer with an internet connection and a USB port, you can use Kindle anywhere in the world. You can make purchases from the Kindle Store on Amazon.com (www.amazon.com/kindlestore
), download items to your computer, and transfer the files to your Kindle using the USB connection. You can access all your purchases from the Kindle Store in Your Media Library at www.amazon.com/library