No-one accuses non-unionised workers of driving down wages by taking low-paid jobs. So why are migrant workers who do accused of undermining pay and conditions? Migrants just want to earn a living and, like everyone, would love to have better pay and conditions. Many of them would like to organise to improve pay and conditions for all.
Immigration controls prevent people working legally and make them vulnerable to super-exploitation. The direct effect is to undermine the pay and conditions of migrants, and then all workers. To improve pay and conditions in sectors where there are many migrant workers, offer them solidarity. Organise with them and oppose immigration controls which hinder resistance.