Background: The COVID-19 pandemic is rapidly evolving, with emerging variants and fluctuating control policies. Real-time population screening and identification of groups in whom positivity is highest could help monitor spread and inform public health messaging and strategy. Methods: To develop a real-time screening process, we included results from nose and throat swabs and questionnaires taken 19 July 2020-17 July 2021 in the UK's national COVID-19 Infection Survey. Fortnightly, associations between SARS-CoV-2 positivity and 60 demographic and behavioural characteristics were estimated using logistic regression models adjusted for potential confounders, considering multiple testing, collinearity, and reverse causality. Findings: Of 4,091,537 RT-PCR results from 482,677 individuals, 29,903 (0·73%) were positive. As positivity rose September-November 2020, rates were independently higher in younger ages, and those living in Northern England, major urban conurbations, more deprived areas, and larger households. Rates were also higher in those returning from abroad, and working in healthcare or outside of home. When positivity peaked December 2020-January 2021 (Alpha), high positivity shifted to southern geographical regions. With national vaccine roll-out from December 2020, positivity reduced in vaccinated individuals. Associations attenuated as rates decreased between February-May 2021. Rising positivity rates in June-July 2021 (Delta) were independently higher in younger, male, and unvaccinated groups. Few factors were consistently associated with positivity. 25/45 (56%) confirmed associations would have been detected later using 28-day rather than 14-day periods. Interpretation: Population-level demographic and behavioural surveillance can be a valuable tool in identifying the varying characteristics driving current SARS-CoV-2 positivity, allowing monitoring to inform public health policy. Funding: Department of Health and Social Care (UK), Welsh Government, Department of Health (on behalf of the Northern Ireland Government), Scottish Government, National Institute for Health Research.