Safe in the UK.
Not if the UK fully commits in the event of a war and they pull conscription out of the bag.

After all, you already have assets committed to helping out somewhere in their neck of the woods.
there aren't any roads or trains between north and south are there? I don't think there are, and I feel stupid for asking, but I figured I should ask the question.
Well I can't imagine any reason anyone from either side would want to cross over, unless it's North to South.
Is there even any evidence that North Korea could feasibly deploy a tactical nuclear device? There's a big difference between conducting an underground test and being able to mount one on a missile.
If they have that capability, it will almost definetely be used against South Korea, Seoul, more specifically.
The only feasible strategy for the South's survival in a war, is if the South initiate the contact, and eliminate at least 90% of the North's missile batteries. If the North initiate the contact, then Seoul is almost definetely going to bite it.