There was never any nuclear exchange because a nuclear exchange with all of today's arsenal would [b][i]physically destroy the planet[/i][/b]. This is not a post-apocalyptic scenario. Corporations are still there, North America has unified, lasers and railguns are a thing, and society is pretty much just as strong. Once people realize that Wales wants to kill all the English, they'll be stomped on easily by thousands of bombers, battleships, and tanks. And those battleships will be using railguns, you know, those things that go as fast as Apollo 11 on reentry. Although, that would be hilarious to watch.
"Sir, the Welsh seem to be on a genocidal rampage."
"Bleh, just bomb' em back to the Dark Ages... OH WAIT!"
And then the attack would be delayed because everyone would be laughing at how stupid the Welsh are. I feel like throwing them back a thousand years isn't the best way to make the point that the Welsh shouldn't be the laughingstock of the world.