Nuclear power can play a role in reducing CO2 emissions and improving energy security. Public attitudes to nuclear safety governance will be critical in whether a large-scale rollout of nuclear power will be successful, so we commissioned a survey of 1,007 members of the British public to understand the determinants of such views. In particular, we focus on the role of trust in government, which has been largely neglected as a subject of study. We find that higher risk perceptions of new nuclear power technologies is associated with lower overall government trustworthiness, while higher engagement levels, being male and intentions to vote Conservative increase trustworthiness. Risk perceptions towards old and the new nuclear technologies do not differ significantly, which raises questions about the view that newer defence-in-depth nuclear technologies can reduce public fear of nuclear power. To build public trust, the UK government must demonstrate its trustworthiness in nuclear safety governance, especially along the dimensions of integrity, reliability and openness. Further, improving stakeholder engagement and thus increasing the levels of public satisfaction towards the government are necessary. Our novel research methodology of determining government trustworthiness in relation to public risk perceptions, technical knowledge, and stakeholder engagement is more broadly applicable and can be transferred to other subject areas and to countries where public concerns over nuclear safety and energy security are significant.