This paper estimates the welfare effects of Brexit, focusing on trade and fiscal transfers. We use a standard quantitative general equilibrium trade model with many countries and sectors and trade in intermediates, as in \citet{CR2014}. We simulate a range of counterfactuals reflecting alternative options for EU-UK relations following Brexit. Welfare losses for the average UK household are 1.3 if the UK remains in the EU's Single Market like Norway (a ``soft Brexit''). Losses rise to 2.7% if the UK trades with the EU under World Trade Organization rules (a ``hard Brexit''). A reduced form approach that captures the dynamic effects of Brexit on productivity more than triples these losses and implies a decline in average income per capita of between 6.3% and 9.4%, partly via falls in foreign investment. These negative effects are widely shared across the entire income distribution and are unlikely to be offset from new trade deals.