WASHINGTON — When people discuss the stakes of Britain’s decision to leave the European Union, they often talk about implications for the “European project,” the continuing post-World War II effort to unify the Continent politically and economically. But within hours of the polls’ closing on Thursday, it appeared that something much more basic could be at risk: Britain as a multinational state.

The United Kingdom of Great Britain and Northern Ireland, as it is formally known, is one of only a handful of countries that consist of multiple nations, politically and legally distinct but united under a common government.

That system of government has been the subject of far less frenzied commentary than European unity, because it is smaller, and because it has seemed so stable. But the crisis-ridden, relatively young European Union may well outlast the 300-year-old United Kingdom, a prospect that speaks to both the underappreciated audacity of Britain’s multinational experiment and the strength of the forces that could now put it to an end.

There has long been political jostling among the four nations that constitute the United Kingdom, but the so-called Brexit referendum has divided them in ways that mean they may not come back together again. England and Wales voted to leave the union. Scotland and Northern Ireland voted to stay. Within hours, Scottish and Irish politicians raised the possibility that their nations would leave the United Kingdom so they could remain in the European Union.