Emerging evidence indicates that for some people, the COVID-19 lockdowns are a time of high risk for increased food intake. A clearer understanding of which individuals are most at risk of over-eating during the lockdown period is needed to inform interventions that promote healthy diets and prevent weight gain during lockdowns. An online survey collected during the COVID-19 lockdown (total n = 875; analysed n = 588; 33.4 ± 12.6 years; 82% UK-based; mostly white, educated, and not home schooling) investigated reported changes to the amount consumed and changes to intake of high energy dense (HED) sweet and savoury foods. The study also assessed which eating behaviour traits predicted a reported increase of HED sweet and savoury foods and tested whether coping responses moderated this relationship. Results showed that 48% of participants reported increased food intake in response to the COVID-19 lockdown. There was large individual variability in reported changes and lower craving control was the strongest predictor of increased HED sweet and savoury food intake. Low cognitive restraint also predicted greater increases in HED sweet snacks and HED savoury meal foods. Food responsiveness, enjoyment of food, emotional undereating, emotional overeating and satiety responsiveness were not significant predictors of changes to HED sweet and savoury food intake. High scores on acceptance coping responses attenuated the conditional effects of craving control on HED sweet snack intake. Consistent with previous findings, the current research suggests that low craving control is a risk factor for increased snack food intake during lockdown and may therefore represent a target for intervention.