My local LTNs are in Hackney, and I know of other similar schemes in Islington and Camden, and I guarantee after a life time of working in Social Housing in most of the Central London Boroughs, that there will be high numbers of social housing within those LTNs. And I'd hazard a guess that elsewhere in the country, where LTNs exist or are being planned, there will be social housing contained within. I'm not sure if it still exists , but in the premier street in my home town, The Royal Crescent, in Bath, there was a council flat on that street.