The main reason the Brexit campaign is making progress is because they are convincing people that leaving the EU would give us control of our borders and allow us to exclude east European immigrants. It will do no such thing.
Even Brexiters admit that if we leave the EU our economic survival will continue to depend on access to the European free market. That means we will have to join the European Economic Area, just like Norway and Switzerland. A condition of that membership is acceptance of EU rules on migration (and some other things). The result would be that we would have less control, not more, over immigration policy. Instead of being one of the biggest EU countries making any changes to the rules, we would be outsiders, bound by rules in which we have no say at all.