I'm not so sure about that. Wage suppression in certain sectors was blamed rightly or wrongly on EU (mostly Eastern) migrants. The irony being that those from places like Poland and Hungary were not happy when FOM was extended to Romania and Bulgaria!!
At least British businesses were quick to raise wages when we left the EU, so British people could finally earn what they were worth.
I get that some people might have been upset, such as plumbers, decorators and electricians, where there was suddenly a lot more competition and not the usual wage structure (indeed, a lot of the work is carried out cash in hand and off the books) but people must have been foolish to think we'd suddenly see huge pay rises once there were fewer workers.
I know there were some exceptions, like lorry drivers, albeit with one off bonuses to entice people rather than massive per-hour increases, but for the most part we now have loads of vacancies and existing workers made to cover multiple roles and work much harder for less.
Meanwhile, the Government was hoping to push forward to make changes that would make things worse for workers and allow companies to get even cheaper labour from outside the EU, and tell existing 'natives' that they better accept the same, or less, money because they can easily be replaced.
It seems such plans may be delayed now with a change of PM and the evidence showing they can't hope to push through such changes now a lot of the workforce have shown they've had enough and are willing to strike - with the majority of the public backing it.
That and a Government almost certain to lose the next election, so having to be a little more pragmatic.
I don't know what will happen, but I think we're bound to be seeking to rejoint he EU within the next 5-20 years, and that will start with frictionless trade and freedom of movement.