I decided to give this a try. I subscribe to a VPN service. If you aren't familiar with what this is, the important part for this discussion is that I can make myself appear to be from different geographic locations.
In this case, the service has a London server so I used that making it appear I was in London. I then signed in to my US Amazon account. I tried a streaming video from Amazon Prime and a movie (Despicable Me 2) I had in my Amazon account. Neither worked, giving me a permissions/location error.
So it would seem what you suggested wouldn't work. However, if you were to sign up with a VPN service that has US servers, you could flip that situation around. The VPN would allow you to appear to be from the US. However, I am guessing you would need a credit card with a US billing address. Or possibly you could buy an Amazon gift card in the UK and gift it to the US account.
As an example, while connected to the London server, I was able to stream content using the BBC's iPlayer. The quality was very good.
Edit: Seem's like Joshua's answer is easier.
As far as I'm concerned, it's a damned shame that a field as potentially dynamic and vital as journalism should be overrun with dullards, bums, and hacks, hag-ridden with myopia, apathy, and complacence, and generally stuck in a bog of stagnant mediocrity. - Hunter S. Thompson, 1958, from cover letter he wrote for a newspaper job.