That assumes that the UK is one of the combatants in the 3rd WW.The major cities in a nuclear war would include ones that house the governments that have access to nuclear weapons. You bomb your political (and militaristic) enemies first.
That would include London.
I really believe that when Riker said "most of the major cities have been destroyed and there are few governments left" that he was talking only about the cities and governments of the combatants, and not generally.
If there is a world wide transporter system, then I would imagine that ease of travel would be a given, people might use it for relatively short distances. However I don't know that people would be able to "work from anywhere," Some people (most?) would still be working in a set location.In a future where you could work from anywhere and energy is cheap, I imagine there being much more mobility overall.
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