Consider this. Singapore has a migrant population of 43% vs UK 13%. Singapore has one of the highest home ownership rates in the world. Why? Because of their housing policy. In Singapore you will live longer, be less obese, make twice as much money, less likely to be unemployed, pay less tax, less likely to die at infancy, spend less on healthcare. That's with x4 the amount of immigration. Migration has nothing to do with the problems you're talking about, you could triple migration with no issues if you actually build for it. UK isn't even in the top 20 of countries when looking at migrants as a percentage of the population.
We have an aging population so our tax revenues will drop as less people are in the workforce, less people spending on goods and services. Without migrants we would not be meeting the replacement rates as more people are dying than being born in the UK. Do you understand that we actually need more young people?
I'm not even sure that you're British tbh given your spelling of "labour". The irony that you are using the American version, are you a migrant?