And how would you do it?

There was plenty of discussion of the consequences, heck, the remain campaign focused more or less ONLY on the consequences of the EU's economic retaliation.

Leaving the EU will absolutely allow immigration to be pushed down, though likely not to the "tens of thousands per year" figure that seems to have been arbitrarily chosen simply because that'd result in too many very useful and in-demand people being excluded. But the type of immigration that has caused so much malcontent in the regions can absolutely be close to eliminated, i.e. poor unskilled workers coming from eastern Europe and undercutting the wages of the locals.