And people forget that cheap labor creates lower prices on the market. Are you willing to pay more even double the price for a commodity just because it was made by non-immigrants?
Not to mention, that most immigrants aren't staying for long term. They go do the work, generate GDP and after a few years they go back to friends and family. Very few have the intentions to stay.
Is it the EUs fault that British stores and businesses buy the goods from low cost EU countries? If you would have a grocery store, would you buy and sell food that was produced in Britain, but comes with a much higher cost, or would you get it from somewhere else cheaper and get it without the costs of shipping from country to the other because of the free trade?
The EU helps everyone, but it's not their fault if businesses use these to their advantage.
Hate the player and not the game, as they say.