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Transmission of SARS-CoV-2 without symptoms is well described, and may be mitigated by mass testing. Nonetheless, the optimal implementation and quantitative real-world impact of this approach remain unclear. During a period of rising SARS-CoV-2 prevalence, students at the University of Cambridge were enrolled in a voluntary programme of weekly PCR-based asymptomatic screening. Swab pooling by household reduced the total testing capacity required by five-fold, without affecting laboratory workflows or compromising test sensitivity. Participation remained >75% throughout the study period. 299/671 (45%) of students diagnosed with SARS-CoV-2 were either identified or pre-emptively quarantined because of the screening programme. After a negative screening test, the risk of developing COVID-19 over the following 7 days was decreased by 51%. Modelling transmission using parameters from our study suggests a reduction in R0 of up to 31% attributable to weekly screening. We therefore demonstrate the feasibility and efficacy of regular, voluntary mass testing for COVID-19.