Background: Approval for the use of COVID-19 vaccines has been granted in a number of countries but there are concerns that vaccine uptake may be low amongst certain groups. Methods: This study used a mixed methods approach based on online survey and an embedded quantitative/qualitative design to explore perceptions and attitudes that were associated with intention to either accept or refuse offers of vaccination in different demographic groups during the early stages of the UK's mass COVID-19 vaccination programme (December 2020). Analysis used multivariate logistic regression, structural text modeling and anthropological assessments. Results: Of 4,535 respondents, 85% (n = 3,859) were willing to have a COVID-19 vaccine. The rapidity of vaccine development and uncertainties about safety were common reasons for COVID-19 vaccine hesitancy. There was no evidence for the widespread influence of mis-information, although broader vaccine hesitancy was associated with intentions to refuse COVID-19 vaccines (OR 20.60, 95% CI 14.20–30.30, p < 0.001). Low levels of trust in the decision-making (OR 1.63, 95% CI 1.08, 2.48, p = 0.021) and truthfulness (OR 8.76, 95% CI 4.15–19.90, p < 0.001) of the UK government were independently associated with higher odds of refusing COVID-19 vaccines. Compared to political centrists, conservatives and liberals were, respectively, more (OR 2.05, 95%CI 1.51–2.80, p < 0.001) and less (OR 0.30, 95% CI 0.22–0.41, p < 0.001) likely to refuse offered vaccines. Those who were willing to be vaccinated cited both personal and public protection as reasons, with some alluding to having a sense of collective responsibility. Conclusion: Dominant narratives of COVID-19 vaccine hesitancy are misconceived as primarily being driven by misinformation. Key indicators of UK vaccine acceptance include prior behaviors, transparency of the scientific process of vaccine development, mistrust in science and leadership and individual political views. Vaccine programmes should leverage the sense of altruism, citizenship and collective responsibility that motivated many participants to get vaccinated.