LONDON — Blowing past another deadline, Britain and the European Union said Sunday they have made enough progress in their seemingly endless trade and security talks to continue negotiations into the coming days.

Many had feared Sunday was the final hour to reach a Brexit deal, but the talks will roll on. Businesses on both sides of the English Channel, fearing chaos at the ports and steep, immediate tariffs, sighed a collective “Whew, that was close!”

Still, British Prime Minister Boris Johnson, in a TV address, did not sound optimistic. “I’m afraid we’re still very far apart on some key things,” he said. “But where there is life, there’s hope; we’re going to keep talking to see what we can do. The U.K. certainly won’t be walking away from the talks.”

Johnson warned “the most likely” outcome would see Britain depart the European Union without a deal, leaving it to trade on what the prime minister insists on calling “Australian terms,” which really means defaulting to do business by the rules set by the World Trade Organization.

Europe is Britain’s largest trading partner; reverting to WTO rules would mean taxes, or tariffs, on exports sold to the continent. The average WTO tariff is less than 3 percent. But for automobiles, it’s 10 percent, and for fresh meat — such as Welsh lamb — it’s 38 percent or more.

Johnson might have been jostling for position. Or he might have been warning the nation.

“The best thing to do now, for everybody, is to follow up all the work that has been done over the last four and half years, colossal amount of preparation at our ports, everywhere across the U.K., get ready to trade on WTO terms,” he said. “There is a clarity and a simplicity in that approach that has its own advantages. It is not where we wanted to get to, but if we have to end up with that solution, the U.K. is more than prepared.”

Whether Britain is prepared to have its imports and exports subjected to border controls, inspections and tariffs is unknown. Many predict chaos at the ports.

European Commission President Ursula von der Leyen was slightly less gloomy. She said it was worth trying to struggle onto a finish line. “We had a useful phone call this morning. We discussed the major unresolved topics,” she said.

Then she patted both sides on the back. “Our negotiating teams have been working day and night over recent days,” she said. “And despite the exhaustion after almost a year of negotiations, despite the fact that deadlines have been missed over and over, we think it is responsible at this point to go the extra mile.”

And so, “we have accordingly mandated our negotiators to continue the talks and to see whether an agreement can even at this late stage be reached.”

The negotiations will continue, at least for now, in Brussels. Britain exits the European Union at midnight on Dec. 31.

Irish Foreign Minister Simon Coveney, a close observer of the talks, told the national broadcaster RTE on Sunday that “a deal can be done, but it really needs to be done within the next few days.”

Jitters over a no-deal “hard Brexit” have been dialed up, regardless.

The Guardian newspaper reported the British government “warned supermarkets to stockpile food and other essential supplies amid increasing fears of a no-deal Brexit in less than three weeks’ time.”

On the Sunday morning TV talk shows, Foreign Secretary Dominic Raab sought to assure Britons that there would be enough medicines and vaccines in the country no matter what because the government had already begun to amass supplies.

Meanwhile, Johnson’s government announced that four Royal Navy patrol ships would be ready to protect the country’s fishing grounds in the event of a no-deal Brexit. The vessels would be given the authority to board and impound European fishing boats inside Britain’s 200-mile exclusive economic zone.

European Council President Charles Michel, on French radio on Sunday, said the sides should keep calm and carry on. “The U.K. and Europe are friends, partners, allies, and it will be the case after Brexit. I encourage everyone to remain calm. I would not say, like Donald Trump, that our boats are bigger than theirs, because I’m trying to be serious, but, on the European side at least, we remain calm. . . . We are reasonable. We want to have close links with the U.K.”

The impasse and issues have not changed over these many months. Britain wants to be able to “take back control” of its sovereignty — for many Brexiteers, that was the whole point of leaving the bloc. Johnson and his allies say it makes no sense to leave the customs union and single market, only to have to continue to align in lockstep with E.U. regulations over state subsidies, labor laws and environmental regulations.

But Europe has appeared in little mood for compromise — especially over these “level playing field” challenges.

The disagreements have touched on areas that have been sore points for years — in some cases, centuries — such as fisheries, specifically European access to British waters.

Beyond wrangling over cod and scallops, which represent far less than 1 percent of the gross domestic product to either Britain or Europe, the E.U. doesn’t want Britain undercutting it on issues such as state aid or environmental regulations to gain a competitive advantage. It wants to make sure British rules stay closely aligned with E.U. ones as a prerequisite for Britain to get relatively unfettered access to the European market.

Ariès reported from Brussels.