The final post on that thread brought it to mind.
I remember it being mentioned on a thread or three a couple of years back.
Basically a website, like a marketplace, where excess social housing (mostly northern) was available via direct application? Does anyone else remember?
Obviously it's a big move and not easy, but if the OP from the benefits cap thread or anyone else trapped in a similar bind felt up to a bold move, it could be an option.