The major concern was the free movement of people I believe, and there have been overtures and whispers that this type of immigration could continue after Brexit so your implication that free movement may stay after negotiations could very well be on the cards. This however could be a time bomb for the Tories having swept up ukip votes and in the end not delivering. May could actually deliver a soft Brexit if she doesn't get the result she wants through the ballot box, and a soft Brexit isn't a Brexit it'll be the concessions Cameron was after before the EU slapped him down and sent him off with nothing. I don't trust the Tories one iota but out of all the parties they have the closest idea of what many leave voters consider a viable extraction from the EU. My only worry is that the Tories wont solve the unfettered access to this country for EU migrants in the same way she and the Tories didn't solve the immigration numbers from outside of the EU.