The Covid-19 pandemic raised many societal problems, one of them being convincing people to comply with government measures to control its spread. In the UK, many unprecedented measures were taken to that end. Public health bodies often use fear appeals to encourage people to obey the rules. What happens though when individuals hold beliefs contrary to government narrative? In this study, the relationship between coronavirus induced anxiety and compliance behavior over the first UK lockdown is examined in relation to general conspiratorial beliefs and specific Covid-19 conspiracy myths. Results suggest a small interaction between specific Covid-19 conspiracy beliefs and anxiety, and that while for most, increased anxiety enforces compliance, for those with conspiratorial beliefs regarding Covid-19 (but not general conspiratorial beliefs), this may not be true. Fear appeals may be successful for the majority, but a small minority may continue to ignore advice. Implications for public health are discussed.