Yes, so maybe the user-agent string has something to do with it, even if both Surface 2 and your PC have "identical" IE11. The Surface IE sends a particular user-agent string with a touch token and I think an ARM string as well; there have been other issues with IE11 on Surface sending people to mobile/broken versions of websites instead of the proper landing page. Speaking theoretically, of course.
Edit to add: I had no idea that Amazon Prime Instant Streaming was a brand-new thing in the UK.
Lovefilm Instant becomes Amazon Prime Instant Video in the UK
I wonder if there's some technical thing going on in relation to LoveFilm and the new Ama Prime branding....
I don't really know. But yeah Amazon Prime started just a few days back. I have the Prime membership for free delivery which is now being carried forward till next year - so Prime Videos/ Movies are free for 1 year. After than the price goes up. On balance, I think I will opt for Netflix because (1) they have a dedicated app for the Surface and (2) they seem to have a better selection than Amazon.