I would say New England is more like 関東 or 関西, a region.
首都圏 strikes me as similar to saying the New York metropolitan area.
Completely agree,yes. I was just trying to convey generally that there are lots of cases of names for areas which most people (that live there) all understand, but which do not map to official or legal boundaries. New York metro area is a good example.
I always have fun trying to explain to people that Tokyo is not a city 
Ah, I see what you were getting at. Though in this case, there actually is a law that defines it.