I'm not so sure, BWM. Certainly, that is an effect. It may also be part of the answer to the question "why now?" and also what kind of Brexit. But if I was that influential I would try to get it decided by Parliament rather than put it to a popular vote which most pollsters thought they would lose. You also have to take into account the anti-immigration rhetoric has been going pretty much since the EU was created, decades before the proposed tax regulations.