Well, they already had homes. For which they paid a portion of their daily labour to the state in the form of rent.

In exchange, they paid a (usually larger) portion of their daily labour to banks in the form of mortgage payments.

So the outcome of selling council housing was a massive transfer from the state to bank shareholders.

Yes, the worker gained an asset. So the state transferred that asset to the worker for a consideration that is worthless to the state (money is no use to the government). But the rent payments are also an asset, and that was transferred to bank shareholders, for no consideration at all.

Now there are many fewer council homes. So workers cannot access affordable housing. Some of those who were able to buy their "own homes" have housing but those new to the market have no access to stock. Unless the people who bought the houses are able to rent them housing.

Which is undesirable. Because when you pay rent to the government, the money is destroyed and leaves the system. If it's paid to a local council, it subsidises the council's provision of services so that the government can make other spending choices. But if you pay rent to a private landlord, the money is not destroyed and does not help the government make other spending choices. In fact, the government will usually have to subsidise the private landlord in one way or another at a rate equivalent to the difference between the council rent and the private rent (and this happens with assistance that tops up rents such as housing benefit or rental assistance).

So the government at the same time gave up a way to relieve inflationary or at least spending pressures while helping to create asset inflation, which itself increases the transfer of wealth from those who do not own assets to those who do.

None of this was an accident. And when Thatcher pushed these policies, she knew very well what she was doing: at the same time transferring wealth to your "betters" *and* crimping the ability of the state to help you.