As for fixing the job market, we need to raise the status of the low-status jobs rather than consider people as commodities where you can just get another source rather than solving the supply issues. Importing people straight into the lower classes will just grow the lower classes, with all the downsides that has to offer; crime, prostitution, political or religious extremism, etc.
One thing at the time: Make working in a nursing home an acceptable occupation rather than something that's done by the most desperate. Service personel should be valued, rather than threatened or constantly pushed down. When the guy who pays someone else to mow his lawn stops looking down on the guy who mows it, that's when we can start considering attracting foreign labour to fill positions. If it's still a problem at that point.
Or field work. Or nursing, in the sense of general nursing duties not necessarily high paying theatre and post operative recovery nursing, although Britain needs them too. No, I absolutely do mean the disgusting, dirty, low paid menial jobs that western working class poor people won't do.
That's the story of migration to the USA, the ubiquitous Mexican labour in hotels, cleaning, cafes and bars, meat works that keeps America working.
I absolutely agree "flooding" the market won't help. I'm talking about a 25 to 50 year problem here.
All migrants are exploited at some level, even H1B. They need unions as much as anyone else.
You're not wrong about the next five years. There's going to be a lot of racism at play, and right wingers like Orban and Le Pen will make much of it.
But the underlying economic truth I believe in remains: the west needs migration more than most people realise, and immigration and refugee law is regressive and unhelpful.