The UK exit from the European Union (Brexit) is likely to have a range of impacts, with trade flows likely to be most affected. One possible outcome of Brexit is a situation where WTO tariffs apply to merchandise trade between the UK and the EU. By examining detailed trade flows between the UK and all other EU members, matching over 5200 products to the WTO tariff applicable to external EU trade this paper shows that such an outcome would result in significantly different impacts across countries. Our estimates of exposure at the country level show an extremely wide range with reductions in trade to the UK falling by 5% (Finland) to 43% (Bulgaria) taking into account the new tariffs and the elasticity of the trade response to this price increase. Food and textiles trade are the hardest hit, with trade in these sectors reducing by up to 90%.