Something to keep in mind is the categorization of labor has more than one purpose, here you are focused on a specific purpose that a government might use in a visa scheme. But many economists are doing it to track the availability, wage levels, growth or contraction, etc of various jobs and it can be difficult to prepare meaningful data if you want to fight all day about “all jobs are skilled.” Well, to an economist trying to prepare a report on if a college education provides a good return on value, he needs to do some delineating.
FWIW I don’t really have a ton of issue with some of the goals of your government, I do not think the primary way that working class jobs should be filled is through cheap imported labor. I’m generally in favor of robust immigration, but I’m not in favor of immigration simply being a gift to corporations to hurt domestic working class people. This 100%, absolutely has happened in the United States, and I would be surprised if it has not happened in the UK. In fact while I have less knowledge of the UK, I absolutely know that it has happened in the UK as well, stories of Northern , West Midlands etc industrial cities that have lots of formerly employed factory workers who no longer have jobs reach the United States.
Many times the policy wonks and the elite have largely said “oh well, remember, our policies are creating more net jobs, and on net, they benefit more people.” That is usually also true, but when the people who are fucked completely and have their lives ruined during the “transition”, for far too long policymakers have assumed those people will “just adapt.” It is difficult to just adapt when you’ve worked a working class job in a specific town your whole life and that is taken away from you, and the only viable alternatives are lower paying service industry jobs or moving across country where you might lose the resources of an extended family, might have to sell the family home and be unable to afford one in the new destination etc etc.
What’s interesting in the United States is the sort of industrial jobs we have basically moved out of the Rust Belt and now staff significantly with imported labor, were quite deliberately located in places other than the Rust Belt–because the Rust Belt tends to have laws that strongly protect unions, the States the jobs were moved to do not. So even if a Rust Belt worker was willing to relocate to take a job in Tennessee or South Carolina they would almost certainly be paid a lower wage, with less safety and job protections.
It’s a complicated issue, both the US and UK have in common that our domestic populations do not satisfy all of our job needs, but at the same time we have lots of disadvantaged working class people either out of work, or who have permanently left the work force (retired early, living on benefits etc) because of poor prospects. You can find stories in the United States about counties with high unemployment that host things like chicken processing factories, where most of the jobs are held by immigrants (very often illegal.) The business owners will say that they need the immigrant labor because there are “no Americans willing to do the work.” The reality is there probably would be, but these chicken processing plants are horrific places to work that pay terribly, so for someone with roots in the community they might rather rely on the support base they have and work lower paying service jobs to avoid the hell of the chicken plants. But if the chicken plants actually paid a higher wage, it is quite likely many of those people would reconsider them. On some level the ability of the business to use the (often illegal) immigrant workforce lets them keep wages at levels that are not attractive to Americans…but that isn’t fairly considered “Americans won’t do the work”, no–it’s more that “Americans won’t do the work at a level that your shareholder driven values will support.”