Rent controls used to work fine until the Thatcher regime abolished them along with minimum space standards. Minimum space standards have now returned thankfully so maybe rent controls will also make a comeback.
I do like the irony that it has been some years since we could have afforded to buy the house we currently live in but I don't think selling off the remaining stock of social housing will fix that. I also can't see the idea of moving all of Londons poor to the empty North and moving affluent young folk into their slab blocks is the way forward as it will be a long commute back for them to clean the offices, serve the coffees and sweep the streets of the capital. Shared equity seems like a good way of subsidising the cost of housing for the young but is really just a different form of in work benefit and fails to tackle the real issue which is the divisive inequality which has grown up in our society in my lifetime. When I was young those on average incomes could easily aspire to own a house but currently my children will have to wait until we expire to have any chance of even getting started unless the multiplier becomes 10x or more the annual salary.