This wouldn't have mattered, I think. The houses were sold at a massive discount, IIRC.
The kind of mass sell-off that occurred could only be considered a massive failure. Selling individual properties at market value when the intention is to reinvest that money is clearly without objection. But to this day, the government offers discounts of up to 70% on social housing. It is a direct transfer of public wealth into private ownership and it has invariably led to worse outcomes where it has occurred. Social housing, royal mail, and water infrastructure are the obvious examples but less obviously there's PFIs, energy, and the nhs.
This is too broad a category. You can't criticise people owning homes by using examples of private(ish) ownership of infrastructure.
So build denser, taller housing. We sprawl massively compared to developments on the continent.
> a non-negligible portion of society are unable to afford market rates
If we increase supply, market rates will fall. That's how markets work.
Therein lies the real problem, of course: real estate investors with existing holdings don't want the rates to fall, and they have influence over how much new stock gets built.
> It was a colossal failure
To be clear, the failure was not in the act of selling itself, but in the decision to not reinvest the proceeds into new housing stock. This is the part that made the housing problem worse instead of better.