That’s true. There is no way they can build enough houses for all the migrants in the UK. They could not build enough fast enough. But they don’t want to face that problem.
Interesting UK birth/death and migration data here -
https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationestimates/articles/overviewoftheukpopulation/mar2017#why-is-the-population-growing