By voting to leave the European Union (EU) in 2016, the United Kingdom (UK) set off a long period of uncertainty and signalled its support for the Leave campaigns, which centred around restricting migration. This paper researches how this decision affected EU-UK migration patterns. We exploit the Brexit referendum as a natural experiment and employ a (synthetic) difference-in-differences estimator to compare EU migration (treated) to non-EU migration (untreated) in the UK. We find a significant decrease in the inflow of EU migrants, although the reduction seems too small to have any impact on the migrant stock. We further find a significant persistent rise in British citizenship applications and grants. Our results reveal that the referendum made the UK a less attractive destination and that the EU migrants already in the UK were encouraged to obtain British citizenship. The Brexit-induced policy uncertainty was the key driver affecting migrants' decision-making.