The Brexiters have pushed the idea that migration leads to low wages. Boris Johnson notoriously attempted a Bank of England Report (
The impact of immigration on occupational wages: evidence from Britain) in support of that claim which Alex Salmond was able to counter that in fact it showed that overall the effect on wages of migration was miniscule. Overall. However, the report did show that for every increase of the proportion of migrants of 10% wages fell by 1.9%. 10% is the equivalent to going from 10% to 20% these quite large changes but 1.9% is not insignificant.