The COVID-19 pandemic has seen digital contact tracing emerge around the world to help prevent spread of the disease. A mobile phone app records proximity events between app users, and when a user tests positive for COVID-19, their recent contacts can be notified instantly. Theoretical evidence has supported this new public health intervention1-6, but its epidemiological impact has remained uncertain7. Here we investigated the impact of the NHS COVID-19 app for England and Wales, from its launch on 24 September 2020 through to the end of December 2020. It was used regularly by approximately 16.5 million users (28% of the total population), and sent approximately 1.7 million exposure notifications: 4.4 per index case consenting to contact tracing. We estimated that the fraction of app-notified individuals subsequently showing symptoms and testing positive (the secondary attack rate, SAR) was 6.0%, comparable to the SAR for manually traced close contacts. We estimated the number of cases averted by the app using two complementary approaches. Modelling based on the notifications and SAR gave 284,000 (108,000-450,000), and statistical comparison of matched neighbouring local authorities gave 594,000 (317,000-914,000). Roughly one case was averted for each case consenting to notification of their contacts. We estimated that for every percentage point increase in app users, the number of cases can be reduced by 0.8% (modelling) or 2.3% (statistical analysis). These findings provide evidence for continued development and deployment of such apps in populations that are awaiting full protection from vaccines.