LONDON — It can be hard, in the climactic days of a high-stakes negotiation, to separate theatrics from substance — and so it was on Saturday evening, when Prime Minister Boris Johnson of Britain and the president of the European Commission, Ursula von der Leyen, hung up after an hourlong phone call.
Ms. von der Leyen said Britain and the European Union would send their negotiators back to the table in a last-ditch effort to close the gaps holding up an agreement on their post-Brexit trading relationship. Mr. Johnson’s aides released a vivid photo of him on the phone, gesturing in the glare of an old-fashioned desk lamp, like a wartime prime minister battling on behalf of his country.
On Monday, the two leaders will speak again to determine whether a deal can be struck by a Dec. 31 deadline. If not, the European Union will begin imposing tariffs on British goods. Four and a half years after Britons voted narrowly to leave the union, the final act of the long-running Brexit drama is at hand.
With the outcome so uncertain, Britain and the European Union are preparing their domestic audiences either for a landmark accord that will require compromise on both sides — or for a breakdown that will disrupt cross-channel trade, pitching both Britain and Europe into uncharted territory.
Nobody disputes that there are genuine differences between the two sides, ranging from state aid to fishing rights.
“There is still some distance to travel, and the distance has yet to be traveled, because it involves concessions that are painful,” said Mujtaba Rahman, an analyst at the political risk consultancy Eurasia Group. “That’s part of the reason both sides have a vested interest in being seen to be fighting.”
That is especially true of Mr. Johnson, who won election last year by promising to “get Brexit done.” Under the terms of the withdrawal agreement he signed with Brussels, Britain formally left the European Union last January. But it agreed to abide by the bloc’s rules and regulations for an 11-month transition period until the two hammered out more permanent trade arrangements.
Now, Mr. Johnson will have to decide whether the European Union’s demands are too much of a threat to his vision of British sovereignty. He knows that striking an accord that is seen as a betrayal of Brexit could be toxic, wrecking his relations with the faction of the Conservative Party that helped him to power. The same Brexiteers ruthlessly disposed of Mr. Johnson’s predecessor, Theresa May.
After months of grinding negotiations, the two sides are wrestling over the same issues that have divided them from the start: state aid to industries — known as the “level playing field” — and European Union access to British fishing waters.
Fishing has become a charged issue as President Emmanuel Macron of France, facing his own next election in 2022, has pushed for continued access for French fishing fleets. Mr. Johnson has made big promises to his country’s fishermen, who have complained for years about sharing Britain’s waters with continental boats, which in some areas can catch much more than British ones.
Although economically insignificant — its annual contribution to Britain’s economy is less than that of the fashionable London department store Harrods — the fishing industry is politically totemic because of its importance to coastal towns, where there are few other sources of employment.
Last week, the French prime minister, Jean Castex, visited the port of Boulogne-sur-Mer, in France’s far north, to reassure fishermen. The country’s Europe minister, Clément Beaune, warned that Paris would veto any unsatisfactory trade deal. Because Britain sells much of the fish it catches inside the European Union, analysts believe a deal is in the interests of both sides and will therefore not be the cause of a collapse.
Perhaps harder to bridge is the gap over rules on fair competition, an issue where the two sides are still talking past each other.
Mr. Johnson says that since Britain wants only a basic free trade deal — similar to the one Canada struck with the European Union — Britain should not be tied to European rules. But officials in Brussels fear that Britain, as a large economy on Europe’s doorstep, could adopt lower labor or environmental standards, flood the European market and undercut continental companies.
Mr. Johnson appears willing to preserve existing standards that Britain agreed to as a member of the European Union, but not to adopt ones that Brussels might put in place in the future. For him, analysts said, this is a question of sovereignty and independence, which he views as the prime dividend of Brexit.
Yet the fear in continental Europe is that this could effectively give Britain a veto over future European policy. For ambitious leaders like Mr. Macron, that would threaten the sovereignty of the European Union at a time when he and others are seeking a more muscular role in the global economy.
“It’s about the E.U. being a geopolitical platform in the world, having a voice in the competition with China and in its relationship with the new Biden administration in the U.S.,” Mr. Rahman said.
Mr. Johnson must also consider his relations with President-elect Joseph R. Biden Jr., who opposed Brexit.
The Johnson government recently introduced legislation giving it the power to renege on parts of its withdrawal agreement with the European Union that deal with Northern Ireland. That antagonized the Europeans, but it also ruffled Mr. Biden, because such moves could lead to the return of a hard border on the island of Ireland.
Mr. Biden warned Mr. Johnson not to do anything in his Brexit negotiations that would threaten the Good Friday Agreement, which ended decades of sectarian violence in Northern Ireland. If London and Brussels strike a trade deal, Mr. Johnson would almost certainly remove the offending language from the legislation.
In the meantime, however, his ministers insist they will go ahead with the Northern Ireland bill, which is scheduled to return to the House of Commons on Monday. That could inject another combustible element into the talks. With time running out, analysts are nervous that any miscalculation could lead to a breakdown in talks with the European Union.
“If both sides were prepared to jump on an equal basis, you could see a deal,” said David Henig, director of the U.K. Trade Policy Project at the European Center for International Political Economy, a research institute.
“Any prime minister would prefer a deal,” Mr. Henig added, “but Boris Johnson has backed himself into a big corner — and while all logic runs toward an agreement, momentum and emotion are running against.”