The COVID-19 epidemic can probably be ended and normal life restored, perhaps quite quickly, by weekly SARS-CoV-2 RNA testing together with household quarantine and systematic contact tracing. Isolated outbreaks could then be contained by contact tracing, supplemented if necessary by temporary local reintroduction of population testing or lockdown. Leading public health experts have recommended that this should be tried in a demonstration project in which a medium-sized city introduces weekly testing and lifts lockdown completely. The idea was not considered by the groups whose predictions have guided UK policy, so we have examined the statistical case for such a study. The combination of regular testing with strict household quarantine, which was not analysed in their models, has remarkable power to reduce transmission to the community from other household members as well as providing earlier diagnosis and facilitating rapid contact tracing.