I don't follow your logic sometimes. The problem is that this is complex and is being used as political propaganda(not least by me). Most Muslim families tend to have larger families(contraception banned) especially toward the more fundamentalist. So many now have 4 to 6 children, either sharing one or two bedrooms in those style flats all over the country. Many of the blocks are also dumping housing for drug addicts and a few sad deviants. I think a family for the health of their children need a house with a garden, and a safe environment. But people like Blair have no idea of consequences.
So they need to build a massive amount of houses not only for the millions of people invited here by Blair/EU, and all their children. But also for those displaced and all the young couples here who are desperate to get out of the rent trap. I don't believe there are any empty houses, the demand is fierce. The housing market is now a financial investment system, if the UK build millions of houses, the demand and therefore price of existing stock will drop.