On Friday the European Union leaders emphasized that there must be no backsliding on that deal, adding in a set of guidelines that “negotiations in the second phase can only progress as long as all commitments undertaken during the first phase are respected in full and translated faithfully into legal terms as quickly as possible.”

The early focus of those second-phase talks will be on a transitional program to cover the period immediately after March 2019 when Britain is to quit the bloc. During that time, which Mrs. May wants to limit to two years, very little will change in the relationship in order to give time to prepare for a potentially big shake-up in trade rules.

British businesses in particular are eager to have certainty that there will be a transition, rather than a sudden rupture — considered a “cliff edge” departure — from the bloc. To achieve that, Britain will have to accept all the rules of the European Union, including the remit of the European Court of Justice, during the transitional period.

But the bigger challenge is clinching a long-term agreement for a deep free-trade deal, given the constraints imposed by Mrs. May, who says Britain must leave the European Union’s single market and customs unions, which remove barriers to trade, and eliminate tariffs and customs checks.

Jean-Claude Juncker, president of the European Commission, said he expected formal discussions on future trade talks to start in March. While some British business leaders fret about the continuing uncertainty implied by such a delay, diplomats say they expect unofficial, exploratory exchanges over trade to begin earlier.

Mr. Rutte, the Dutch prime minister, said that it was now incumbent on Mrs. May to tell the other leaders what kind of trading relationship she wanted. He noted that she had been “holding her cards close to her heart,” adding that this had so far been “probably a wise negotiating tactic,” but one that would not hold for much longer.

Ms. Merkel reinforced that message, adding that it was not up to the European Union to lay out possible solutions to a problem created by Britain’s 2016 referendum decision to quit the bloc. “Britain has to tell us what it wants,” she said.