Investigations about mental health report prevalence rates with fewer studies investigating psychological and social factors influencing mental health during the Covid-19 pandemic. (1) identify sociodemographic groups of the adult population at risk of anxiety and depression and (2) determine if the following social and psychological risk factors for poor mental health moderated these direct sociodemographic effects: loneliness, social support, threat perception, illness representations. Cross-sectional nationally representative telephone survey in Scotland in June 2020. If available, validated instruments were used, for example, Patient Health Questionnaire (PHQ-4) to measure anxiety and depression. Simple linear regressions followed by examination of moderation effect. A total of 1006 participants; median age 53 years, 61.4% female, from all levels of area deprivation (i.e., 3.8% in the most deprived decile and 15.6% in the most affluent decile). Analyses show associations of anxiety and depression with sociodemographic (age, gender, deprivation), social (social support, loneliness) and psychological factors (perceived threat and illness representations). Mental health was poorer in younger adults, women and people living in the most deprived areas. Age effects were exacerbated by loneliness and illness representations, gender effects by loneliness and illness representations and deprivation effects by loneliness, social support, illness representations and perceived threat. In each case, the moderating variables amplified the detrimental effects of the sociodemographic factors. These findings confirm the results of pre-Covid-19 pandemic studies about associations between sociodemographics and mental health. Loneliness, lack of social support and thoughts about Covid-19 exacerbated these effects and offer pointers for pre-emptive action. © 2021. The Author(s).