Their big fear is that two years of negotiation will fail to yield a trade deal, leading to a “cliff edge” plan in which import and export tariffs are applied with little time to prepare.

On Wednesday David Davis, the minister responsible for negotiating British exit, suggested that a transitional arrangement might be possible to overcome the risk of such economic disruption, providing that the broad outlines of the final deal are settled by the end of the two-year period.

“If you build a bridge, you need to have both sides established before you build the bridge,” he told lawmakers, while adding that it was “perfectly possible to know what the end game will be in two years.”

Alongside the chancellor of the Exchequer, Philip Hammond, Mr. Davis is emerging as a more pragmatic force in the internal British cabinet discussions, for example, keeping open the option that Britain might be willing to continue making some budget contributions to the bloc after Brexit, in exchange for privileges.

More surprisingly, Mr. Davis also referred to the possibility that Britain might, legally, be able to revoke its decision to quit the European Union, once it had ignited exit talks under Article 50 of the European Union’s treaty — though he added that this was not something he anticipated. Until now, the government has argued that once started, the process could not be reversed.

Inside the British government, civil servants are working frantically to assess the potential economic impact of Brexit on different sectors of the economy, as their political masters struggle to assemble a strategy for Brexit talks.

So far Britain has not said formally that it wants to leave the European Union’s customs union, which provides for tariff-free trade, or its single market, which removes non-tariff barriers, and Mrs. May argues that there need be no “binary choice” between being on the inside or the outside.