I agree that we need to build more social housing - of course we do. Not only would it provide housing, but it would provide work.
The trouble is that housing in the UK is a classic case of market failure, which is why the state needs to intervene. The market dictates rents and landlords will get what they can. I don't agree that housing benefit is pushing up rents for most housing, because there are plenty of potential tenants who will pay. The real problem is a supply one, which is why rent caps won't work.
The situation is likely to get worse, because the fall in sterling is pushing up opportunities for foreign investment.
Nobody is talking about 'fault', but we have a situation where taxpayers are paying for people to live in accommodation which is too big for their needs, while those who need family-sized accommodation are forced to rent privately or with friends/relatives and are effectively homeless. It's an ineffecient use of public resources and not fair.
The petition was about pensioners in social housing. Ironically, they're the one group which is still protected. The real poverty is being experienced by people of working age on low incomes or unemployed, but nobody seems to care much about them.