Contemporary policy and scholarship recognises an important and enduring relationship between cultural heritage and human rights. However, despite this broad recognition, the mobilisation of cultural heritage as a right has been lacking application, structure or sustained interrogation, particularly in contexts where peoples and their heritages are vulnerable. Based on participatory ethnographic work on the asylum applications of the Somali Bajuni campaigners in Glasgow, UK, this paper explores the extent to which the rights-based discourses involved in cultural heritage and in seeking asylum can(not) speak to each other. In a detailed consideration of the Bajuni campaigners' cases, the paper traces how top-down definitions of the campaigners' intangible cultural heritages are used to persistently deny them asylum in the UK. Taking its cue from the campaigners' own arguments, and drawing on decolonising scholarship, the paper argues that an emphasis on grounded, minority-group led definitions of heritage is a vital part of the process that sees cultural heritage fundamentally embedded in discourses about human rights.