This paper proposes a new panel data structural gravity approach for estimating the trade and welfare effects of Brexit. The suggested Constrained Poisson Pseudo Maximum Likelihood Estimator exhibits some useful properties for trade policy analysis and allows to obtain estimates and confidence intervals which are consistent with structural trade theory. Assuming different counterfactual post-Brexit scenarios, our main findings suggest that UK's exports of goods to the EU are likely to decline within a range between 7.2 percent and 45.7 percent (EU's exports to UK by 5.9 percent to 38.2 percent) six years after the Brexit has taken place. For the UK, the negative trade effects are only partially offset by an increase in domestic goods trade and trade with third countries, inducing a decline in UK's real income between 1.4 percent and 5.7 percent under the hard Brexit scenario. The estimated welfare effects for the EU are negligible in magnitude and statistically not different from zero.