ABSTRACT. It might be thought that Brexit is just a case of the UK getting honest with itself and its partners. On that interpretation, much British opinion never really accepted European integration. Hence, the UK should never have joined a body committed to an “ever closer Union between the peoples of Europe.” Yet, I argue, the relationship of the UK to the process of European integration has been complex and paradoxical. As a member of the EU, the UK promoted a major act of European centre formation: namely, the formation of the single market. Even where they felt unable to participate in other initiatives – such as monetary union and Schengen – British Governments settled for largely constructive forms of abstention. One thing the UK has not been is a significant constraint, or source of fragmentation in the process of European integration. That may not even change with the vote in June 2016 to leave the Union. Continued UK participation in aspects of European integration cannot be ruled out. Nor can a failed exit from the Union. On the one hand, Brexit seems both necessary and impossible: something the UK has to do and something that it cannot do. On the other hand, there seems to be no stable equilibrium in British politics for any one approach to Brexit. Yet, if it cannot “exit,” the UK may have to seek more “voice” and “loyalty” in its relationship with the Union. I make this argument by reviewing some of the history and contemporary political science of the UK’s relationship with the European Union in what, I hope, are mutually helpful ways.