I think it would be done, but a few things of note should be addressed:
Firstly, there would need to be some sort of equivalent of Vault-Tec in the UK. This is perfectly plausible, after all there are nuclear bunkers in Britain. In fact there is one just over an hours drive from where i live.
Fallout's aesthetics may have to be modified for Britain. America's aesthetics are 1950's esque, and i think you could do similar for the UK. In Resistance 1, there were elements of British 1950's-1960's architecture. You could create good gaming environments with rows of terrace houses and towering, crumbling concrete blocks of flats.
But, i think if you went for a more neo-Victorian Steam-Punk theme then that would be better and give the game more style unique to Britain whilst making it stand out from it's American counterpart. Plus, like how Fallout 3 harps back to the American "Golden Age", a Fallout in Britain would do likewise for Britain's "Golden Age" with environments full of Imperial pomp and decadence, steam powered machinery, airships and Victorian fashion. Britain also has the advantage of having more history, so you could have gaming environments set in stately homes and medieval castles. There would also be more medieval weapons such as cannons, longbows, pole arms, swords, axes, armour et cetera would be more plentiful than in America.