BACKGROUND: In the absence of a vaccine, governments have focused on social distancing, self-isolation, and increased hygiene procedures to reduce the transmission of SARS-CoV-2 (COVID-19). Compliance with these measures requires voluntary cooperation from citizens. Yet, compliance is not complete. Existing research on the predictors of compliance is almost exclusively based on cross-sectional data, raising the possibility of reverse causality and confounding. METHODS: Using data from the UCL COVID-19 Social Study, a large weekly online panel of UK adults from first three months of lockdown in the UK (n = 51,600), we tested whether within-person changes in confidence in government, mental wellbeing, social experiences and awareness of COVID-19 were longitudinally related to self-reported compliance levels with guidelines from authorities using random intercept cross-lagged panel models. FINDINGS: We found evidence of a small longitudinal association between increased confidence in government to tackle the pandemic and higher self-reported compliance, but little evidence that factors such as mental health and wellbeing, worries about future adversities, and social isolation and loneliness were related to later compliance. We found higher self-reported compliance was longitudinally related to higher depressive symptoms. We found that low compliance was related to lower leisure engagement, providing care, and working outside the home. INTERPRETATION: Our results suggest that to effectively manage the pandemic, governments should ensure that confidence is maintained. FUNDING: Nuffield Foundation, Wellcome Trust and the MARCH Mental Health Network. MARCH is funded by the Cross-Disciplinary Mental Health Network Plus initiative supported by UK Research and Innovation.