Just caught up with this and earlier I googled 'is council housing subsidised', and it seems there is space for debate about it, with valid points on both sides.
I appreciate that many (not all) council or ha tenants may now have paid off the cost of their build and therefore are genuinely only paying for their own running costs, and I'd just like to point out that I have never been under the impression that social housing is for people that don't work! I appreciate it's not a subsidy in the form of money being exchanged in favour of the tenant to pay their rent, and a tenant may be paying out quite a significant chunk of their income on rent.
Private landlords and homeowners have to charge enough to pay the tax they are charged on their rental income, or on buying their property, or paying the bank. These are costs that a social tenant and their landlord do not need to cover, despite those costs being essential to society.
Social and private rents are based on completely different, but equally valid methods of housing. A HA that is a charity will get tax exemption in much the same way that a private school will.
Whether you think that is a subsidy or not depends on your interpretation of the word subsidy.
Personally I think having a social tenancy is enough of an advantage that anyone who holds one should consider themselves one of the lucky few.