The availability of a COVID-19 vaccine has been heralded as key to controlling the COVID-19 pandemic. COVID-19 vaccination programme success will rely on public willingness to be vaccinated.We used a multi-methods approach - involving an online cross-sectional survey and semi-structured interviews - to investigate parents' and guardians' views on the acceptability of a future COVID-19 vaccine. 1252 parents and guardians (aged 16 + years) who reported living in England with a child aged 18 months or under completed the survey. Nineteen survey participants were interviewed.Most survey participants reported they would likely accept a COVID-19 vaccine for themselves (Definitely 55.8%; Unsure but leaning towards yes 34.3%) and their child/children (Definitely 48.2%; Unsure but leaning towards yes 40.9%). Less than 4% of survey participants reported that they would definitely not accept a COVID-19 vaccine. Survey participants were more likely to accept a COVID-19 vaccine for themselves than their child/children. Participants that self-reported as Black, Asian, Chinese, Mixed or Other ethnicity were almost 3 times more likely to reject a COVID-19 vaccine for themselves and their children than White British, White Irish and White Other participants. Survey participants from lower-income households were also more likely to reject a COVID-19 vaccine. In open-text survey responses and interviews, self-protection from COVID-19 was reported as the main reason for vaccine acceptance. Common concerns identified in open-text responses and interviews were around COVID-19 vaccine safety and effectiveness, mostly prompted by the newness and rapid development of the vaccine.Information on how COVID-19 vaccines are developed and tested, including their safety and efficacy, must be communicated clearly to the public. To prevent inequalities in uptake, it is crucial to understand and address factors that may affect COVID-19 vaccine acceptability in ethnic minority and lower-income groups who are disproportionately affected by COVID-19.