Widespread vaccination uptake has been shown to be crucial in controlling the COVID-19 pandemic and its consequences on healthcare infrastructures. Infection numbers, hospitalisation rates and mortality can be mitigated if large parts of the population are being vaccinated. However, one year after the introduction of COVID-19 vaccines, a substantial share of the Swiss population still refrains from being vaccinated. We analysed COVID-19 vaccination uptake during the first 12 months of vaccine availability. We compared vaccination rates of different socioeconomic subgroups (e.g., education, income, migration background) and regions (urban vs rural, language region) and investigated associations between uptake and individual traits such as health literacy, adherence to COVID-19 prevention measures and trust in government or science. Our analysis was based on self-reported vaccination uptake of a longitudinal online panel of Swiss adults aged 18 to 79 (the "COVID-19 Social Monitor", analysis sample n = 2448). The panel is representative for Switzerland with regard to age, gender, and language regions. Participants have been periodically surveyed about various public health issues from 30 March 2020, to 16 December 2021. We report uptake rates and age-stratified hazard ratios (HRs) by population subgroups without and with additional covariate adjustment using Cox regression survival analysis. Higher uptake rates were found for individuals with more than just compulsory schooling (secondary: unadjusted HR 1.39, 95% confidence interval [CI] 1.10-1.76; tertiary: HR 1.94, 95% CI 1.52-2.47), household income above CHF 4999 (5000-9999: unadj. HR 1.42, 95% CI 1.25-1.61; ≥10,000 HR 1.99, 95% CI 1.72-2.30), those suffering from a chronic condition (unadj. HR 1.38, 95% CI 1.25-1.53), and for individuals with a sufficient or excellent level of health literacy (sufficient: unadj. HR 1.13, 95% CI 0.98-1.29; excellent: HR 1.21, 95% CI 1.10-1.34). We found lower rates for residents of rural regions (unadj. HR 0.79, 95% CI 0.70-0.88), those showing less adherence to COVID-19 prevention measures, and those with less trust in government or science. Vaccination uptake is multifactorial and influenced by sociodemographic status, health literacy, trust in institutions and expected risk of severe COVID-19 illness. Fears of unwanted vaccine effects and doubts regarding vaccine effectiveness appear to drive uptake hesitancy and demand special attention in future vaccination campaigns.