It took a while, but British government ministers finally got their messages aligned over the past week over an issue many businesses regard as vital. Finally speaking with one voice, they said Britain would seek a multiyear transitional agreement with the European Union to reduce the economic uncertainty around Brexit.

From either side of the Brexit divide inside Prime Minister Theresa May’s government, ministers publicly backed an intermediate period post-Brexit before the U.K. fully separates from the EU. That would help firms adjust to leaving the bloc’s regime of zero tariffs and common regulation, and provide time for customs and other parts of the bureaucracy to cope.

They found common cause partly in recognition that it would be impossible, in the 20 months left before Brexit, to negotiate a wide-ranging permanent trade and economic agreement with the EU and have it ratified by the more than 30 national and regional parliaments that must do so.

In fact there was unity only up to a point. On Thursday, immigration minister Brandon Lewis suggested the matter wasn’t yet settled when he told the British Broadcasting Corp. that “Free movement of labor ends when we leave the European Union in the spring of 2019.”

If Mr. Lewis is really ruling out free movement of labor from the EU on Brexit day, he is also probably ruling out the most likely and practical transition deal with the EU, one that would keep the U.K. temporarily inside the bloc’s single market and its customs union.

The EU insists that free movement of goods, services, capital and labor come as a package. If you want to stay in the EU’s single market and enjoy free movement of services, goods and capital, as many businesses are demanding in the transition, then labor comes as part of the deal.

True, that EU proposition could be tested in the negotiations. But it would be tough for London to persuade the bloc to make concessions to a nonmember of the EU, which the U.K. will become on Brexit day, that it wouldn’t concede to a member of the club.

The U.K. could try to negotiate a bespoke interim arrangement, sector by sector, issue by issue. But the Confederation of British Industry, which lobbies for British business and says a transitional deal keeping the U.K. in the single market and customs union is an urgent priority, has joined other observers in reaching a firm conclusion on that prospect: “It is hard to see how this could be negotiated in time and it may not provide a sufficient legal basis for business continuity in many sectors.”

Unlike a wide-ranging permanent arrangement that would require time-consuming ratification, legal experts think a time-limited transitional deal could be appended to the divorce agreement. That would require only the consent of a qualified majority of the 27 remaining EU national governments and a simple majority of the European Parliament.

The real problem with a transitional arrangement has lain with Britain’s most eager EU-leavers, many of whom are in the governing Conservative Party. For them, staying in the customs union and single market would extend the agony of the jurisdiction of the European Court of Justice that polices the single market, and mean Britain would have to keep making accommodations for EU workers.

It would also mean continued U.K. contributions into the EU budget—a prospect Brexiteers hate but that provides a big incentive for the EU to accept a transition. Such a deal would keep a large net payer in the fold for a while longer and postpone a big impending fight between net contributors and recipients of EU funds over the bloc’s shrinking spending pot.

It would also take some of the steam out of the argument over the British “divorce bill”—the financial settlement the EU wants from the U.K. over spending pledges it has made but won’t have carried out by Brexit day.

The EU’s unofficial calculations of upward of €60 billion ($70 billion) for that bill include U.K. spending commitments for the current seven-year EU budget period through 2020. If the U.K. stays in the single market and customs union until then, keeping the British government’s budget contribution at current levels would require it to pay more than €20 billion of the bill anyway.

A transition would also likely mean delaying the implementation of any trade agreements the U.K. negotiates with non-EU countries such as the U.S. Since customs unions impose common tariffs on goods coming from outside, members can’t negotiate away tariffs with third parties.

Ministers have been talking of a three-year transition, allowing the U.K. to be free of its EU entanglements by the next scheduled U.K. general election in 2022.

U.S. President Donald Trump might thus be able to sign a trade accord with the U.K. during his first term of office. But he would have to win the 2020 presidential election to oversee its implementation.