Housing associations have always been private bodies. They have a number of areas of business, depending on the association, but traditionally they rent property and build property. This new build property is usually sold either outright or as shared ownership, and a (say 20-50%) portion will be more rented stock.
Housing associations haven't been able to build more houses for a variety of reasons, and this has contributed to the housing shortage over time as house associations provide a hugely amount of new homes in the U.K.
In 2015 HAs were reclassified as public bodies to follow accounting regulations -
www.publicfinance.co.uk/news/2015/10/housing-associations-classified-public-bodies
This has now been reversed, probably because it was stupid. They claim it will increase house building and there are reasons why it may, mainly because Moody's reduced HAs credit rating on the back of them being made public bodies.
It didn't affect HAs operations and still doesn't.