This paper examines a behavioural explanation for the Brexit referendum result, the role of an individual's inequality aversion (IA). We study whether the referendum result was an "unconsidered Leave" partially driven by people's low aversion to inequality. We use a representative sample of the UK population fielded in 2017, and analyse the extent to which lottery-based individual IA estimates predict their Brexit vote. We consider alternative potential drivers of IA in both income and health domains; these include risk aversion, locus of control, alongside socio-economic and demographic characteristics. A greater aversion to income inequality predicts a lower probability of voting for Leave, even when controlling for risk aversion and other drivers of the Brexit vote. This effect is only true among men, for whom an increase in income IA by one standard deviation decreases their likelihood of voting for leaving the EU by 5% on average. Had there been a greater IA, the overall referendum result might have been different. However, the effect of health inequality aversion is not significantly different from zero.