There's a saying that you can't make someone understand something if it's not in their financial interest to understand it. So I expect this post to have no impact on a lot of previous posters in this thread...
My definition of subsidy is getting something for free, or for a payment of less than it is worth. (If you don't want that to be the definition of subsidy, then tell me a different word that means what I mean by it and I will use that instead.)
Where social rents are less than private rents would be, for the same property let on the same terms, the person paying the social rent is being subsidised. The size of the subsidy is the amount their rent is below the market rent. If London social housing were not being subsidised, there would be no waiting lists. Waiting lists are how a non-market system matches supply to demand, in a market system the price fluctuates to the correct level, that being the one that causes supply and demand to be matched.
If the social housing tenant also receives housing benefit, then they are getting two different kinds of subsidy at the same time. My preference would be for their to be only one system of subsidy, and housing benefit is far more open, honest and transparent than giving people subisidised housing for a long time because they managed to work their way to the top of a waiting list at one point in their lives.
I will be happy when all council housing is let at market rents. I don't care if all the extra rent is paid by housing benefit: my priority is financial integrity and honesty, I don't have any strong opinion on how much overall subsidy there should be for housing.