We develop a network trade model with country-sector level input-output linkages. It includes (1) domestic and global value chain linkages between all country-sectors, (2) direct as well as indirect shipments (via other sectors and countries) to a final destination, (3) value added rather than gross trade flows. The model is solved analytically and we use the sectoral World Input Output Database (WIOD) to predict the impact of Brexit for every individual EU country by aggregating up the country-sector effects. In contrast to other studies, we find EU-27 job losses to be substantially higher than hitherto believed as a result of the closely integrated EU network structure. Upstream country-sectors stand to lose more from Brexit due to their network centrality in Europe. JEL-Codes: C530, D570, F170, F140.