Understanding the drivers for spread of SARS-CoV-2 in higher education settings is important to limit transmission between students, and onward spread into at-risk populations. In this study, we prospectively sequenced 482 SARS-CoV-2 isolates derived from asymptomatic student screening and symptomatic testing of students and staff at the University of Cambridge from 5 October to 6 December 2020. We performed a detailed phylogenetic comparison with 972 isolates from the surrounding community, complemented with epidemiological and contact tracing data, to determine transmission dynamics. After a limited number of viral introductions into the university, the majority of student cases were linked to a single genetic cluster, likely dispersed across the university following social gatherings at a venue outside the university. We identified considerable onward transmission associated with student accommodation and courses; this was effectively contained using local infection control measures and dramatically reduced following a national lockdown. We observed that transmission clusters were largely segregated within the university or within the community. This study highlights key determinants of SARS-CoV-2 transmission and effective interventions in a higher education setting that will inform public health policy during pandemics.