As someone who has lived in a 'mixed block' in zone 1, I think it's delusional to characterise social housing tenants as 'teachers and nurses'. I suspect most teachers and nurses are already in private sector housing in London.

I think it could be OK to sell all social hosing in Zone 1/2 and use that money to pay higher wages for teachers and nurses plus state built replacement social housing in zone 4-6. There's probably some other space in the welfare system, look at the motability scandal or the increase in PIP claims.