LONDON — As an agglomeration of about 500 million people who speak at least two dozen tongues, the European Union is no stranger to disputes over language.

Yet three short words could determine whether it faces perhaps the biggest rift in its history.

Fresh from its struggles to contain the crisis over Greece, the European Union is seeking to head off the threat of a British exit from the bloc, a move that would reverse decades of progress in knitting its members closer together.

As part of its price for staying, Britain wants an end to a pledge, written into treaties and held dear by advocates of European integration, to strive for an “ever closer union.”

The change is one of the central demands of Prime Minister David Cameron, who has promised to secure a “better deal” for Britain before holding a referendum by the end of 2017 on whether to drop out of the European Union.