Background: People with MS (pwMS) have had higher rates of anxiety and depression than the general population before the COVID-19 pandemic, placing them at higher risk of experiencing poor psychological wellbeing during the pandemic. Objective: To assess mental health and its social/lifestyle determinants in pwMS during the first wave of the outbreak in the United Kingdom. Methods: This is a community-based, prospective longitudinal cohort and cross-sectional case–control online questionnaire study. It includes 2010 pwMS from the UK MS Register and 380 people without MS. Results: The Hospital Anxiety and Depression Scale scores of pwMS for anxiety and depression during the outbreak did not change from the previous year. PwMS were more likely to have anxiety (using General Anxiety Disorder-7) and/or depression (using Patient Health Questionnaire-9) than controls during the outbreak (OR: 2.14, 95% CI: 1.58–2.91). PwMS felt lonelier (OR: 1.37, 95% CI: 1.04–1.80) reported worse social support (OR: 1.90, 95% CI: 1.18–3.07) and reported worsened exercise habits (OR: 1.65, 95% CI: 1.18–2.32) during the outbreak than controls. Conclusion: Early in the pandemic, pwMS remained at higher risk of experiencing anxiety and depression than the general population. It is important that multidisciplinary teams improve their support for the wellbeing of pwMS, who are vulnerable to the negative effects of the pandemic on their lifestyle and social support.