I still have severe doubts this will happen. It will take many years to renegotiate and most treaties will be in effect until then. My guess is very little changes, it's more of a sign that people want their country sovereign as opposed to being ruled by a committee in another country.
To extend your argument, maybe that wouldn't actually change much in the grand scheme of things! But EU regulations have a pretty big impact, so I think the breakup of the EU would actually be a big deal.