The effectiveness of COVID-19 vaccination in preventing new SARS-CoV-2 infections in the general community is still unclear. Here, we used the Office for National Statistics (ONS) COVID-19 Infection Survey, a large community-based survey of individuals living in randomly selected private households across the UK, to assess the effectiveness of BNT162b2 (Pfizer-BioNTech) and ChAdOx1 nCoV-19 (Oxford-AstraZeneca; ChAdOx1) vaccines against any new SARS-CoV-2 PCR-positive tests, split according to self-reported symptoms, cycle threshold value (<30 versus ≥30) as a surrogate for viral load, and gene positivity pattern (compatible with B.1.1.7 or not). Using 1,945,071 RT-PCR results from nose and throat swabs taken from 383,812 participants between 1 December 2020 and 8 May 2021, we found that vaccination with the ChAdOx1 or BNT162b2 vaccines already reduced SARS-CoV-2 infections ≥21 days after the first dose (61%, 95% CI 54 to 68% versus 66%, 95% CI 60 to 71%, respectively) with greater reductions observed after a second dose (79%, 95% CI 65 to 88% versus 80%, 95% CI 73 to 85%, respectively). Largest reductions were observed for symptomatic infections and/or infections with a higher viral burden. Overall, COVID-19 vaccination reduced the number of new SARS-CoV-2 infections, with the largest benefit received after two vaccinations and against symptomatic and high viral burden infections, and with no evidence of difference between the BNT162b2 and ChAdOx1 vaccines.