This article engages with a leading contemporary criticism of social and economic human rights, namely that because such rights are organised around sufficiency norms, they are ill‐equipped to challenge and overturn forms of material inequality. The sufficiency thesis raises issues around the nature of social rights and their capacity to deliver transformative change, and lays a direct challenge to social movements employing human rights talk and practices in campaigns for social justice. This article breaks new ground by taking the right to housing as a case study for assessing the sufficiency thesis. It is argued that while there is some support for the sufficiency thesis in dominant institutionalised legal forms of the right to housing, the wider claim of the thesis, that social rights are incapable of challenging forms of material inequality, does not hold water. This argument is supported by a broad approach to housing rights that engages with the work of the UN Special Rapporteurs on housing and which takes seriously the way in which contemporary social movements in Spain and Scotland employ housing rights in their struggles for housing justice.