Requiring something to be "uniquely British" to count as British cuisine seems like a pretty high bar. Are burgers and apple pie "uniquely American"? Not sure – and who even cares?
You’re right, and that’s not the bad I meant to set. More like cuisine that is associated with Britain. So not a French restaurant that happens to be in London.
My Romanian grandma, born in the 1920s, that never traveled more than 100km from her birthplace and never saw even the Black Sea, would beg to differ :-p
I highly doubt that my almost illiterate grandma, that grew up in interwar Romania and lived afterwards behind the Iron Curtain, discovered apple pie through American media :-))