Moving away from the usual sensationalist statements, I think at a realpolitik level what we are seeing now is an abject failure of government in terms of preparing for life outside the eu. Had we provided more incentives for British firms to hire our native workers for example we wouldn’t be facing the employment shortages we now see.
People are not generally unemployed because they lack access to jobs but because they lack the skills required to do those jobs (or the jobs are not in their area). For instance, across industry there is a huge shortage of people with digital skills and it's hardly as though companies are tight arses not willing to pay to access those skills, it's just that the skills don't exist. For truck drivers it's obviously somewhat different as it's location specific, but for things like digital work, if we don't have the skills here or cannot import the people with the skills, then the work will simply go to where the skills are instead.
Czech is a great example of this in action, as they have almost no unemployment, a prime minister saying they don't want immigration, and a digital skills shortage in the tens of thousands. All it will mean is the jobs will go outside the country.