Amazon's (slightly odd) reply to my question, but it does answer it:
Quote:
Message From Customer Service
Dear Xxxxx,
Please accept my sincerest apologies and my thanks for your continued patience.
I understand from your email that you wish to use 'Prime Instant Video' service in Abroad.
I would like to inform you that Prime Instant Video titles are available to anyone with a UK Amazon Prime or Prime Instant Video membership located in the UK, Isle of Man or the Channel Islands. It isn't possible to access Prime Instant Video titles outside of the UK, Isle of Man or the Channel Islands.
However, you can download videos to a compatible device while still in the United Kingdom, and then play them back on that device from anywhere.
You can view a list of devices capable of downloading videos on our following help page:
http://www.amazon.co.uk/gp/help/cust...deId=201460880
More information about Prime Instant Video is available on our Help pages:
https://www.amazon.co.uk/dv/piv
We value our international customers. I appreciate your thoughts and have forwarded your feedback to the Amazon Instant Video development team.
As a compensation for any inconvenience caused to you recently,* I have requested a 5% refund on your annual subscription fee which is equal to £2.45 and it will be credited to your account within 2-3 working days.
Once again I apologise for the inconvenience caused and thank you for your patience and co-operation in this matter.
We look forward to seeing you again soon.
Warmest regards,
Imran P
Amazon.co.uk
Original Message
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07/20/14 22:02:39
Your name:Xxxxx
Comments ear Support,
I'd like to ask a question about the "Instant Video" service, please. I know that the video streaming service is only available in the UK, but if I buy a video and download it to my iPad, will I be able to watch it on my iPad if I travel to a different country?
Thank you,
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(Emphasis mine). Ie it's exactly as I thought: the service can only be accessed while you're in the UK, but it's fine to download from the UK then playback from elsewhere.