BRUSSELS (AP) — Throwing overboard Sunday’s self-imposed deadline, the European Union and Britain said they will “go the extra mile” to clinch a post-Brexit trade agreement that would avert New Year’s chaos and cost for cross-border commerce.

British Prime Minister Boris Johnson and European Commission President Ursula von der Leyen had set Sunday as the deadline for a breakthrough or breakdown in negotiations. But they stepped back from the brink because there was too much at stake not to make an ultimate push.

“Despite the exhaustion after almost a year of negotiations and despite the fact that deadlines have been missed over and over, we both think it is responsible at this point in time to go the extra mile,” von der Leyen said.

The negotiators were continuing to talk in Brussels at EU headquarters.

European Council President Charles Michel immediately welcomed the development and said “we should do everything to make a deal possible,” but warned there could be a deal “at any price, no. What we want is a good deal, a deal that respects these principles of economic fair play and, also, these principles of governance.”

With less than three weeks until the U.K.’s final split from the EU, key aspects of the future relationship between the 27-nation bloc and its former member remain unresolved.

Progress came after months of tense and often testy negotiations that gradually whittled differences down to three key issues: fair-competition rules, mechanisms for resolving future disputes and fishing rights.

It has been four and a half years since Britons voted by 52%-48% to leave the EU and — in the words of the Brexiteers’ slogan — “take back control” of the U.K.’s borders and laws.

It took more than three years of wrangling before Britain left the bloc’s political structures on Jan. 31. Disentangling economies that have become closely entwined as part of the EU’s single market for goods and services took even longer.

The U.K. has remained part of the single market and customs union during an 11-month post-Brexit transition period. That means so far, many people will have noticed little impact from Brexit.

On Jan. 1, it will feel real. New Year’s Day will bring huge changes, even with a deal. No longer will goods and people be able to move between the U.K. and its continental neighbors.

Exporters and importers face customs declarations, goods checks and other obstacles. EU nationals will no longer be able to live and work in Britain without a visa — though that doesn’t apply to the more than 3 million already there — and Britons can no longer automatically work or retire in the EU.

There are still unanswered questions about huge areas, including security cooperation between the U.K. and the bloc and access to the EU market for Britain’s huge financial services sector.

Without a deal U.K. will trade with the bloc on World Trade Organization terms, with all the tariffs and barriers that would bring.

The U.K. government has acknowledged a chaotic exit is likely to bring gridlock at Britain’s ports, temporary shortages of some goods and price increases for staple foodstuff. Tariffs will be applied to many U.K. goods, including 10% on cars and more than 40% on lamb.

Still, Johnson says the U.K. will “prosper mightily” on those terms.

To jumpstart the flagging talks, negotiators have imposed several deadlines, but none have brought the sides closer together on the issues of fair trading standards, legal oversight of any deal and the rights of EU fishermen to go into U.K. waters.

While both sides want a deal on the terms of a new relationship, they have fundamentally different views of what it entails. The EU fears Britain will slash social and environmental standards and pump state money into U.K. industries, becoming a low-regulation economic rival on the bloc’s doorstep, so is demanding strict “level playing field” guarantees in exchange for access to its markets.

The U.K. government claims the EU is trying to bind Britain to the bloc’s rules and regulations indefinitely, rather than treating it as an independent nation.

Spanish Foreign Minister Arancha Gonzalez Laya said a no-deal Brexit would be a “double whammy” for economies already battered by the coronavirus pandemic.

“It is clear when you do a trade deal that you are a sovereign nation; they are made to manage interdependence,” she told Sky News. “The U.K. and the European Union are interdependent so let’s do a deal which reflects the need to manage this interdependence.”

Britain’s belligerent tabloid press urged Johnson to stand firm, and floated the prospect of Royal Navy vessels patrolling U.K. waters against intruding European vessels.

But others, in Britain and across the EU, urged the two sides to keep talking.

Irish Prime Minister Micheal Martin, whose economy is more entwined with Britain’s than any other EU state, said he “fervently” hoped the talks wouldn’t end Sunday.

“It is absolutely imperative that both sides continue to engage and both sides continue to negotiate to avoid a no-deal,” Martin told the BBC. “A no-deal would be very bad for all of us.”

“Even at the 11th hour, the capacity in my view exists for the United Kingdom and the European Union to conclude a deal that is in all our interests.”

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Jill Lawless reported from London. John Leicester contributed from Paris