You have swallowed their trip, lock, stock and barrel, haven't you. Mos of the immigration is legal, and to fill jobs Brits are unwilling or unable to do.
I remember arriving in a ski resort in the USA- the Mayor and pals had had a massive clean out of much of the migrant workers, some who were illegal, but most who were legit. They were so pleased and proud of themselves! Then ski season started and they realised they had no-one to work in Hôtels, laundery, restaurants and catering, bars, ski lift and snow clearance, patrols, etc. The resort had to close and they lost tons of money and investment. And they didn't have to have staff for care homes, care in the Community, hospitals, etc. The country would fall apart if we sent legal migrants back- and there will be massive shortages if they are not allowed to bring their families with them. Would you move to do a job, and particularly a difficult, perhaps unpleasant one, long hours, low pay AND have to leave your children and spouse behind? Bet you would not. Why should they?
It is the infrastructure that has not been adjusted. Huge new estates with no schools or surgeries, or transport, etc, all over the place. And massive under-investment added to huge cut-backs.