The COVID-19 pandemic has brought about unprecedented global changes in individual and collective behaviour. To reduce the spread of the virus, public health bodies have promoted social distancing measures while attempting to mitigate their mental health consequences. The current study aimed to identify cognitive predictors of social distancing adherence and mental health symptoms, using computational models derived from delay discounting (the preference for smaller, immediate rewards over larger, delayed rewards) and patch foraging (the ability to trade-off between exploiting a known resource and exploring an unknown one). In a representative sample of the UK population (N = 442), we find that steeper delay discounting predicted poorer adherence to social distancing measures and greater sensitivity to reward magnitude during delay discounting predicted higher levels of anxiety symptoms. Furthermore, under-valuing recently sampled information during foraging independently predicted greater violation of lockdown guidance. Our results suggest that those who show greater discounting of delayed rewards struggle to maintain social distancing. Further, those who adapt faster to new information are better equipped to change their behaviour in response to public health measures. These findings can inform interventions that seek to increase compliance with social distancing measures whilst minimising negative repercussions for mental health.