PurposeThe COVID-19 pandemic increased psychiatric distress and impacts differed by family structure. We aimed to identify mechanisms contributing to these inequalities.MethodsSurvey data were from the UK Household Longitudinal Study. Psychiatric distress (GHQ-12) was measured in April 2020 (first UK lockdown;n= 10,516), and January 2021 (lockdown re-introduced following eased restrictions;n= 6,893). Pre-lockdown family structure comprised partner status and presence of children (< 16 years). Mediating mechanisms included: active employment, financial strain, childcare/home-schooling, caring, and loneliness. Monte Carlo g-computation simulations were used to adjust for confounding and estimate total effects and decompositions into: controlled direct effects (effects if the mediator was absent), and portions eliminated (PE; representing differential exposure and vulnerability to the mediator).ResultsIn January 2021, after adjustment, we estimated increased risk of distress among couples with children compared to couples with no children (RR: 1.48; 95% CI 1.15–1.82), largely because of childcare/home-schooling (PE RR: 1.32; 95% CI 1.00–1.64). Single respondents without children also had increased risk of distress compared to couples with no children (RR: 1.55; 95% CI 1.27–1.83), and the largest PE was for loneliness (RR: 1.16; 95% CI 1.05–1.27), though financial strain contributed (RR: 1.05; 95% CI 0.99–1.12). Single parents demonstrated the highest levels of distress, but confounder adjustment suggested uncertain effects with wide confidence intervals. Findings were similar in April 2020 and when stratified by sex.ConclusionAccess to childcare/schooling, financial security and social connection are important mechanisms that need addressing to avoid widening mental health inequalities during public health crises.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12991-023-00454-1.