The cascade of commentary on Britain’s decision to leave institutional Europe has described the epochal event primarily in the vocabulary of calamity. However, the coin of the realm for statesmen is not anguish or recrimination; it should be to transform setback into opportunity.

The impact of the British vote is so profound because the emotions it reflects are not confined to Britain or even Europe. The popular reaction to European Union institutions (as reflected in public-opinion polls) is comparable in most major countries,...