The UK has incorporated the European Convention on Human Rights ("ECHR") through the Human Rights Act 1998 ("HRA"). However, the ECHR mostly deals with civil and political rights rather than economic, social and cultural rights, such as the right to housing. Although the courts have acknowledged that shelter is a basic human right (R (Limbuela) v SSHD [2005] UKHL 66; [2006] 1 AC 396), the European Court of Human Rights has decided that there is no right to housing in the ECHR (Burton -v- UK (1996) 22 EHRR CD 135). However, there is such a right in a number of other human rights instruments:-

• Universal Declaration of Human Rights, Art.25
• International Covenant on Economic, Social and Cultural Rights, Art.11(1)
• Convention on the Elimination of All Forms of Racial Discrimination, Art.5(e)(iii)
• Convention on the Elimination of All Forms of Discrimination Against Women, Art.14(2)
• Convention on the Rights of the Child, Art.27
• Convention Relating to the Status of Refugees, Art.21
• Convention on the Rights of Migrant Workers, Art.43(1) (treaty not ratified by UK)
• European Social Charter (revised), Art.31 (revision not yet ratified)

See my articles  Applying the Right to Housing [2002] JHL 11 and The Other Human Rights [2001] Human Rights 156 as to how the right to housing could be used in English courts.