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Dispute hopes of the two sides could issue a political declaration on Monday, the UK and the EU only agreed to continue “scoping work” to solve the dispute as gaps in their positions remained.
Mr Cleverly and Mr Sefcovic said they would continue to search for potential solutions in a “constructive and collaborative spirit” after they discussed a range of “existing challenges” in the virtual meeting.
There had been speculation the two sides were edging towards technical agreement to ease the implementation of trade checks on good moving between Great Britain and Northern Ireland – but No 10 said there are “still gaps” between the two sides.
Officials could not confirm another meeting had been scheduled, but expected one soon, and they did not say whether talks would enter a more intensive phase.
Irish foreign minister Micheal Martin welcomed the “continued positive engagement”, saying the two sides were working “together constructively to find joint solutions”.
But DUP leader Sir Jeffrey Donaldson also said he believes Brussels and London are not close to striking a deal, describing the difference in viewpoint as “significant”.
The protocol was agreed to by Boris Johnson as prime minister in 2019 as a way of breaking the Brexit deadlock to avoid a hard border in Ireland.
It is still vehemently opposed by many unionists in Northern Ireland, and the DUP is blocking the functioning of a devolved government in Stormont in protest at the arrangements.
On Monday Sir Jeffrey said: “There is still a lot of ground to be covered. I don’t think we are close to a deal at this stage. Our position remains unchanged.”
An announcement last week that a deal had been reached on sharing real-time data on goods travelling from Great Britain to Northern Ireland was seen as a step towards an overall resolution.
But a UK government source played down talk that the two sides were ready to enter the “tunnel” of final negotiations from this week. Mr Sunak’s official spokesman said that “there are still gaps in our position that need to be resolved”.
The role the European Court of Justice in overseeing protocol disputes remains one of the biggest issues for the Sunak government. The two sides are thought to be waiting to see if progress had been forged on the technical trade issues, before trying to hammer out a compromise on the court.
The Sunak government is said to be willing to shelves the controversial bill that would hand UK ministers the power to unilaterally override protocol checks in an effort to reach a compromise deal.
Alongside the UK-EU talks, Labour sent a delegation to Derry to meet business leaders and learn about how the protocol has affected Northern Ireland trade.
The trip will saw shadow foreign secretary David Lammy, shadow Northern Ireland secretary Peter Kyle and shadow Cabinet Office minister Baroness Chapman visit Foyle Port to see “first-hand how red tape from the Conservatives’ deal and ongoing uncertainty are affecting trade”.
Mr Lammy said: “Recent signs of progress on the protocol are promising – Rishi Sunak must press on and stand up to the ERG hardliners before this window of opportunity closes.”
“If the government can reach a deal that delivers for our national interest and the people of Northern Ireland, the Labour party stands ready to do what it takes to get it over the line,” the shadow foreign secretary added.