I'm not sure whether it's even possible to model the passage of a wind reversal down from the stratosphere into the the troposphere. It would be a bit like modelling a ball thrown into a spinning roulette wheel. So even if there were some statistics regarding where the best place would be for a SSW to occur in regard to cold weather in the British Isles, they'd be just that: statistics. And, more to the point, statistics taken from a very tiny sample.
Probably best just to say that a SSW definitely changes things down here at the surface, and from the point of view of what the British winter is usually like, that's got to be a good thing. It couldn't make it any worse, could it?
Mind you, this is all just me thinking aloud. I'd love to know if anyone can answer Hippydave's question more authoritatively.
2 miles west of Taunton, 32 m asl, where "milder air moving in from the west" becomes SNOWMAGEDDON.
Well, two or three times a decade it does, anyway.