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What Brexit is stopping is unemployed immigrants seeking benefits, uncontrolled amounts of cheap unskilled labour or skilled labour that this country does not need.
You think? Successive UK governments already had the scope to reduce the benefits paid to freeloading unemployed immigrants from the EU. They just chose not to bother implementing anything. They also had the scope to reduce immigration of non-EU people and failed to meet their self-declared goals. I don't think you can rely on Brexit to change any of that.
To be open about it, though - I've no problem with controlling immigration of people coming to live and work in the UK. The issue for me is that it has (so far) been one of the underlying principles of being in the EU and I have (a) no desire to see the UK beggared by its own act of leaving and (b) no positive signs or plans or rational proposals from people supporting Brexit that point (a) will not happen. All I hear are statements of faith, much like religious statements of faith. If the UK could stay in the EU and yet control immigration I wouldn't have a problem.
Academic, really, because it seems like we won't really be leaving.