You mean like the majority of other countries around the world?
no, more like the millions of Americans not born in California but have been living here for years or decades suddenly have to apply for a work permit. And millions of Californians who have moved to other states have to do the same.

Full impact of the Brexit is still to be realized but after a few years they will be back in the swing of things and not beholden to the EUs laws.
Businesses who want sell their products in the EU will still have to follow EU regulations, just like foreign companies have to do here.
The primary impact of Brexit is that the UK can strictly regulate immigration from the EU. But then the EU can strictly regulate immigration from the UK. Young Brits won't be able to just get up and move to Madrid or Paris or Berlin and take a job.
For twenty some years, people have been able to move to and from the UK for a job or school or just because they want to just as easily as we can move between US states. Now they will have to ask permission from one government or another.