This is the classic mistake people make who do not work in economic areas.
Artificial labour shortages will ALWAYS lead to reduced output and higher prices. That will then lead to lower economic growth, thus lower tax revenues. Public services will then deteriorate.
See Switzerland. They tried something like Brexit to stop immigratiom and it blew up in their face.
In the case of a builder in a sector who sees a labour shortage now, he will be able to negotiate higher nominal wages, but these will be mostly eroded by higher prices (inflation), thus his real wages did not grow as much.
Very few workers will be able to secure higher real wages (HGV drivers for example are another group that likely will).
In the aggregate, the increase in nominal wages of all of the groups will ALWAYS be beaten by a higher increase in prices (because businesses will cut output and raise prices to survive when they cannot source enough labour to grow), thus leading to a reduction in real wages.
And that is precisely what is happening now. Output is being cut by businesses as they cannot find enough workers, leading to higher prices, whose increase will be higher than any nominal wage increases.
The net effect is that the country as a whole is poorer.
You will see how fast services deteriorate in the UK due to the loss of tax revenus due to lower economic output (and growth).
The reality now is that the UK bar London is in terminal decline due to demographics and poor levels of immigration.
Without immigration the UK is simply poorer.
Thats how it works.