The UK's decision to leave the EU continues to have major economic, political and social implications. It is therefore unsurprising that the reasons behind Brexit have been widely discussed. However, whilst existing empirical evidence has tended to focus on specific factors, we undertake a comprehensive analysis of the leave vote using a large-scale survey dataset to identify the relative importance of key underlying factors. Specifically, we apply regression- based techniques, including decomposition analysis, to quantify the impact of different influences. Our results indicate that a complex range of factors are able to explain a high proportion of differences in the leave vote across sub-groups of the British electorate. Moreover, Brexit voting was underpinned by cultural factors, especially attitudes towards immigration, with educational differences also playing an important role. We find that other influences such as age and economic factors become less important after other influences have been taken into account. Our findings are discussed within the context of some of the economic and social consequences that have emanated from the decision to leave the EU.