EU citizens probably won't event need a visa, just a passport. Especially from rich western EU countries, like it was already the case before Schengen.
The UK is not in Schengen, that's a common misconception :)
One of the points of the Leave campaign, reinforced after the vote by some of its leaders like Michael Gove, is to setup a points system for immigration. If there was no "limit EU migration" argument, Leave would have easily lost the vote.
I know it's not, it's why my wife can't get there :) That's why I said that's how it was even _before_ Schengen, ie French and German didn't need a visa to go to the UK even before the EU.
