Good luck. Would suggest that you contact organisations that have taken action previously against Government about housing, as they will have more information, which will help inform you about best way forward.
Having had a quick look into this, there seems to be quite a lot going on with bedroom tax. Apparently there will be a Supreme Court case at some point. This is a link to an Appeal court case.
http://www.bailii.org/ew/cases/EWCA/Civ/2018/548.html