This paper presents the first detailed and holistic description of the European production network (EPN) and provides different rankings of the most 'systemically important' industries involved in Brexit. Employing techniques of complex networks analysis and Input-Output traditional tools, the study identifies those industries that are key in the complex structure of the UK-EU trade relationships. The method developed would help policy-makers to better understand which tariff would have a more distortive impact, which export sector should be pushed, which imports should be safeguarded. Such information may have foremost importance in the negotiations between the UK and EU. Our findings suggest that Brexit would be not just a problem for the UK, as it is often portrayed, but any form of Brexit could propagate affecting the global production system. Further, by inspecting industries centrality within the EPN, we find that the UK could be less exposed to trade barriers than EU countries.