The problem is that Mr. Johnson’s deal with Brussels, while setting the terms of Britain’s departure from the European Union, resolves none of the fraught questions about the country’s long-term relationship with the bloc, its biggest trading partner. The government would have no more than a few months to settle those questions in a new trade agreement with Brussels, a process that typically takes years.

That means Britain could once again be staring down a catastrophic, cliff-edge split from the European Union in December 2020, when the Brexit transition period is to end. To avoid such a result, Britain could pay the bloc billions of euros a year to hold onto its access to the European market while it completes a long-term, negotiated divorce.

“There is honestly no way to do everything we need to do in 14 months, even with the best of intentions,” said Anna Jerzewska, a trade specialist who has advised the British Chambers of Commerce.

That reality has dawned on Parliament, where lawmakers have already drawn up an amendment to Mr. Johnson’s plan that could protect against an abrupt 2020 exit without a trade agreement by forcing a two-year extension of the transition period.

But such a change could also undercut the support of hard-line Brexiteers and end any hopes of passing a deal now.