Amazon prime

As we know Amazon prime is a bt/plusnet exclusive but say if a customer had a bt box connected to a bt line then changed to a different provider does that mean that the change of IP config would cause Amazon prime to be removed from the box?
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Might it have arrived with a new BT-compatible box from PlusNet?
Or might it just happen to have been released on the same day you switched ISPs?
Amazon hasn't been rolled out to retail boxes yet. I don't know why.
Might be different if you don’t have Amazon Prime anyway.
[Below edited to accommodate redchiz’ pertinent strictures]
The attraction of having Amazon Prime Video on the YouView box, though, for those who have Amazon Prime at all, is that its offerings are seamlessly included in the YouView Search, something you don’t get if your Amazon Prime Video is hosted elsewhere.
For those who aren’t subscribed to it, though, having even more extraneous results is a bloody nuisance....
Though the context of my remarks above was originally just addressing Amazon Prime subscribers, I have accordingly edited them to be fully inclusive of subscribers and non-subscribers alike.