David Cameron promoted a politics of simple solutions, as illustrated by the referendum on EU membership that ultimately undid him. He won two referendums (AV vote and Scottish independence) on the basic premise that voters would stick with the status quo. Similarly, during the EU renegotiation he resorted to a simplistic conceit of talking tough in the hope it might win concessions sufficient to mollify soft Eurosceptics. But the lacklustre outcome derailed the subsequent referendum campaign, which became mired in mendacious claims that were all the more believable for having treated complex policy alternatives as simple choices. This damaging legacy will cast a long shadow over British politics as the country adapts to life outside the EU. However, it also serves as a stark warning to other EU leaders on how not to approach European integration. Hence the political mess occasioned by Brexit might have a positive impact on the EU. The complexity and risks associated with unravelling the UK’s EU membership offer an object lesson to European voters in the limitations of simplistic policy solutions. In this fashion, Brexit can potentially re-affirm European solidarity – at a time of great self-doubt – by highlighting once and for all exactly what would be lost without the EU. Populists have thrived by suggesting that untried solutions are stymied by mainstream ideology, but the throes of leaving the EU could finally reverse this narrative.