THE OVERWHELMING vote by the British Parliament on Tuesday against the painstakingly negotiated accord on the country’s departure from the European Union was all the more devastating because no one — not Prime Minister Theresa May, and certainly not her opponents — has anything with which to replace it. There is, for the moment, no plan or solution that has the support of a parliamentary majority, and E.U. leaders insist they will not accept substantial modifications to the rejected deal.

Brexit has gridlocked the British political system. That means the worst possible option for the country — a crash out of the E.U. without mechanisms for managing it — could happen on March 29. Both Ms. May and her parliamentary opponents must now make it their overriding priority to avoid that disastrous outcome.

Ms. May worked assiduously over 2½ years to square the vision British voters narrowly supported in June 2016 — that the country would regain full sovereignty from the E.U. — with the reality, still unacknowledged by many supporters, that any divorce would involve major economic and political costs. The deal she eventually struck would allow for a transition period during which Britain and the E.U. would negotiate the details of their future trade relationship, while providing that London would regain control over the movement of people across its borders.

Britain’s economy would take a hit from Ms. May’s plan, but the biggest sticking point is how to manage the border between British Northern Ireland and the Republic of Ireland, an E.U. member, so as not to endanger the peace accord that ended decades of violence in the North. To avoid the imposition of a hard border, the E.U. insisted on a “backstop” under which, if no other arrangement were agreed upon, Britain would remain in the E.U. customs union indefinitely. That, in turn, would mean London would have to continue observing E.U. regulations without having input into them and would find it hard to strike trade deals with other countries.

While rejecting that solution, opponents to the left and right of Ms. May have offered no workable alternatives. Instead, they have tried to leverage the Brexit debate to oust the prime minister. Rivals in her Conservative Party tried and failed to do that last month; on Wednesday, the opposition Labour Party will get its chance when Parliament considers its no-confidence motion. Ms. May said that, if the government survives that vote, she will consult with parliamentary leaders on new ideas for a Brexit deal. If there is broad support for any proposals, she said, she will take them to Brussels.

The danger is that there will be no majority in Parliament behind any new proposal — and that E.U. leaders will be unwilling to show flexibility. A statement by European Council President Donald Tusk said the rejected accord “remains the best and only way to ensure an orderly withdrawal.” If those facts don’t change, Britain’s best alternative may be to suspend the withdrawal process and hold another referendum — one in which voters can choose based on the known terms and costs of a deal, rather than the false promises of 2016.

Ms. May, who opposes that option, said following her parliamentary defeat that “every day that passes without this issue being resolved means more uncertainty, more bitterness and more rancor.” That is true, but further disorder for a vital U.S. ally now is unavoidable.

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