BRUSSELS — Effective immediately, leaders of the European Union face one pressing, daunting challenge: how to keep the vision of a united continent from unraveling further, or even self-destructing, after the British people voted to quit. The damning verdict of British voters was the worst setback to the EU since the germ of a more integrated Europe first took shape in the ruins left by World War II. [...] it threatened to be wildly contagious — before the ballots were all tallied, populist leaders in some of the EU’s founding nations were already clamoring for a vote on EU membership in their own countries. With Britain’s departure, the 28-nation EU will have to do without the fifth economy in the world, Western Europe’s No.