A desire to understand the decision of the UK to leave the European Union, Brexit, in the referendum of June 2016 has continued to occupy academics, the media and politicians. Using topological data analysis ball mapper we extract information from multi-dimensional datasets gathered on Brexit voting and regional socio-economic characteristics. While we find broad patterns consistent with extant empirical work, we also evidence that support for Leave drew from a far more homogenous demographic than Remain. Obtaining votes from this concise set was more straightforward for Leave campaigners than was Remain's task of mobilising a diverse group to oppose Brexit.Comment: 17 pages, 4 figures, Preliminary