Most psychological research on Brexit categorises participants as either leave or remain supporters. In the current study we take a data-driven approach and identify different clusterings of attitudes towards the European Union (EU) using latent class analysis (LCA), as well as how these classes differ across a range of important social and psychological variables. This analysis revealed 10 distinct classes of voters in a large (N = 15860) adult sample of UK citizens using data from the British Election Study. These classes ranged from being quite uniformly pro- or anti-EU in sentiment, to more mixed groups with more complex patterns of attitudes. The classes that included majority-remain supporters were younger and better educated, and self-rated more highly on the measures of actively... open-minded thinking, openness, political trust, and external locus of control. The classes that included majority-leave supporters were older and less well educated, and self-rated more highly on the measures of authoritarianism and conscientiousness. However, there were also notable demographic and psychological differences within the classes associated with leavers and remainers. A full consideration of these attitudinal nuances will be necessary to achieve a deeper understanding of why the UK decided to leave the EU.