Whole genome sequencing of SARS-CoV-2 has occurred at an unprecedented scale, and can be exploited for characterising outbreak risks at the fine-scale needed to inform control strategies. One setting at continued risk of COVID-19 outbreaks are higher education institutions, associated with student movements at the start of term, close living conditions within residential halls, and high social contact rates. Here we analysed SARS-CoV-2 whole genome sequences in combination with epidemiological data to investigate a large cluster of student cases associated with University of Glasgow accommodation in autumn 2020, Scotland. We identified 519 student cases of SARS-CoV-2 infection associated with this large cluster through contact tracing data, with 30% sequencing coverage for further analysis. We estimated at least 11 independent introductions of SARS-CoV-2 into the student population, with four comprising the majority of detected cases and consistent with separate outbreaks. These four outbreaks were curtailed within a week following implementation of control measures. The impact of student infections on the local community was short-term despite an underlying increase in community infections. Our study highlights the need for context-specific information in the formation of public health policy for higher educational settings.