For me, instead of blaming immigration for a lack of housing. I'd blame the system that allows people to flip, sell, and own empty homes for investment without the prospect of selling to people who need them. Including a government which has promised but failed to build affordable housing that meets the demands of the UK (and by that I mean actually affordable, as the classification as such is only 80% of standard price). With the government target of 300,000 homes per year being missed by about 50-80,000 homes.