The thing about every sci-fi homage to Omelas is that the forsaken child is doing something. Powering some kind of contraption. Acting as some kind of mega-mind to run the city. Making some kind of unwilling sacrifice "for the greater good."
If Omelas was in Britain then the forsaken child in the pit wouldn't be any kind of keystone or lynchpin to society and its wonders. It'd just be generally reassuring to the populace to know that he was there.