So ... I have two options
Option 1: Retain the Prime subscription, but just delete the Prime Video app from my devices. I don't use the Prime bits of other services like Kindle, Audible, or Music so I'm not losing anything in particular by junking that. I keep the delivery bits.
Option 2: Ditch Prime entirely. Makes sense because I don't watch much on Prime anyway. I'm finding I'm generally using Amazon less anyway: I just don't need to buy very much stuff I don't really need in the normal course of things - so the amount I'm paying doesn't offset what I'd be paying in delivery charges.
Either way, Amazon trying to make me pay extra for a service I'd already paid for isn't making me want to use it any more. Quite the opposite. Mind you, the options suggested by others just to throw their own little spanners in the works make me swell with pride at the lovely contrariness of people here. Least I've got a week or two to decide which to do for my part.