Policies on international student mobility (ISM) have the capacity to structure both flows of students and the representations of globally mobile students through discourse. This paper draws on a text-based analysis of British policy discourses and secondary analysis of published statistics. It uses problematisation analysis to examine how problems and students are represented as social subjects. Growth in student numbers, particularly in high ranking institutions, has coincided with proactive policies over the last 20 years, suggesting that policy discourses are linked to mobility. But policy targets were not met and growth has fallen since the 2010 tightening of migration policy. Nor was the target of diversifying source countries met, meaning the UK remains dependent on student demand from a few nations. This mixed success suggests that student mobility is easily deterred by migration policy, but other policies have little impact on the nature of demand. In interaction with multiple, contradictory media and institutional discourses, policy discourses construct international students as sources of income, immigrants of doubtful value, consumers, and 'other'. These representations may be internalised by students, who learn to subjectify themselves. I call for an approach to ISM which puts statistics in dialogue with discourse.