Employees don't set wage-levels, that is entirely in the hands of employers.

If wage levels have been suppressed over the past period, that is as a result of the behaviour of unscrupulous employers who have taken advantage of the fact that many immigrants arrive from low-wage countries, and have offered lower wage-rates to those workers than they would have otherwise paid.

Several years ago, my company decided to employ a relatively small number of Polish workers because they were having difficulty recruiting employees from our local indigenous population. The immigrant workers were employed on precisely the same conditions of employment as our UK-nationals, and on precisely the same wage-rates as UK-nationals doing the same jobs. Pay rates are based on the job, not on where an employee was born. That is what reputable employers do.

FWIW, the Polish workers involved have proved themselves to be honest, reliable, and hard-working, and are held in high regard by their colleagues and by management.

Instead of blaming immigrants for lowering wage rates, why not put the blame where it rightly belongs - with unscrupulous employers?