As more of us live longer, we continue to live in houses, that someone else would be living in if we were dead.
The smaller house sizes is because more people are living by themselves, families are separating, people aren't living as long with family (ironically that last one is changing for young people, but the driver for new homes is still there). While there are complex stats around ethnicity and housing, one worth noting is that twice as many white people live in single person households, compared with Asian people. Given how the vast majority of the population is white, that's a hugely significant difference.
www.gov.uk
Net migration has never been close to 1.2 million a year. Apart from a couple of recent post-Covid years (when it peaked at 764k with ret), it's maxed out at just over 300k. This year is predicted to be back at around that level.
And, yes, I know your 1.2m ignored emigration, but dismissing emigrants as non-users of social housing, and assuming immigrants are, is just a guess. Given that the 764k was mostly made up of students, and people coming in as workers (many of whom would be covered by the minimum earning levels, or who would be exactly the same kind of mobile higher income workers that you've assumed most emigration involves), there's no reason to presume that they would take up more social housing than those leaving.