On the subject of what the working class think, about immigration or anything else, I am with Sid Vicious, who famously said "I've met the man in the street, and he's a c**t".
The purpose of leadership is exactly that, to lead, not to follow. Especially not to follow the base instinct and ill informed prejudice of the worst of the electorate.
On the subject of public opinion in a democracy btw, I've just finished reading Livy's Early History of the Roman Republic - which I think you'd enjoy, if you haven't already read it. It makes two things abundently clear; first, as Marx observed, all history truly is the history of class struggle. And second, the best recipe for tyranny is a populist leader beloved of the mob.