Anti-Brexit protesters use illuminated signs as they demonstrate outside Parliament on Monday. (Christopher Furlong/Getty Images)

BRITAIN TOOK a step deeper into political turmoil Monday when Prime Minister Theresa May, facing certain defeat, postponed a parliamentary vote on the plan for Britain’s departure from the European Union that she had painstakingly negotiated with E.U. leaders. Ms. May said she would seek “further assurances” from Brussels on the most problematic piece of the agreement, a “backstop” to avoid a hard border between British Northern Ireland and the Republic of Ireland. Critics said it was unlikely she could obtain concessions that would satisfy dissenters in her own governing coalition, much less opponents seeking its ouster from power. Yet no other formula for ending the country’s self-destructive battle over Brexit seemed able, for now, of commanding a parliamentary majority. The likely result is weeks more of uncertainty and bitter debate.

At the heart of the chaos engulfing the United States’ closest ally is the contradiction between the vision sold to voters who supported leaving the European Union in a June 2016 referendum and the reality of the deal Ms. May came home with. Britons were told they could regain sovereignty from E.U. governance without suffering any economic consequences. In fact, any Brexit will leave the country poorer. That is true of the deal being offered by Ms. May. It is even more true of the “no-deal Brexit” that could occur next March 29 if Parliament does not act, causing massive disruption, including shortages of basic goods.

Yet even that is not the most dire prospect. Any deal that leaves Britain out of Europe’s single market could create a border between the two Irelands and threaten the peace accord that ended decades of violence in the North. Ms. May’s plan provides that if Britain and the European Union are unable to agree during a transition period on a relationship that avoids a hard border, Britain would remain in the E.U. customs union indefinitely. That would force London to continue observing E.U. regulations and prevent it from striking its own trade deals with other nations.

Ms. May told Parliament Monday that she would seek pledges from European leaders on limits to this Irish backstop. Yet there is no escaping the underlying reality that a full separation from Europe probably cannot happen without either redividing the two Irelands or drawing a line between Northern Ireland and the rest of Britain.

Rather than accept these facts, Ms. May’s opponents are opportunistically trying to employ them against her. The opposition Labour Party would like to force a new election, while Conservative party hard-liners would like to oust Ms. May. Both insist, implausibly, that they could obtain a better deal, ignoring categorical statements from the European continent to the contrary.

Ms. May evidently hopes that the lack of alternatives will eventually force Parliament to approve her plan. That would explain why she vehemently rejects the growing calls for a second referendum that would allow citizens to choose between the real-world Brexit now on offer and remaining in the union. The prime minister is not wrong in arguing that another popular vote could divide the country and weaken public faith in the political system. It may, however, be the least bad way out of the disaster that Britain has inflicted on itself.