The team – called “Taskforce Europe” – is expected to be operational by 31 January and coincides with the Department for Exiting the European Union (DExEU) ceasing to exist as a Whitehall department.
The new taskforce will be responsible for overseeing the UK’s future relationship with the EU after Brexit, including difficult negotiations about a free trade agreement.
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The Mail on Sunday said the new team will be spearheaded by Mr Johnson and his Europe adviser, David Frost, and will operate out of Downing Street and the Cabinet Office.
“In 2020, we will move forward to establish a future relationship and free trade agreement with the EU,” a source said.
“Following the election, the government has a clear and renewed mandate to achieve this. We want our new relationship to be based on an ambitious free trade agreement, and a close friendship between sovereign equals.”
Following the general election, a government spokesperson confirmed that DExEU, which was created by Theresa May after the referendum, would be wound up once the UK legally severs its ties with the EU on 31 January.
Initially, it had been created to “oversee negotiations to leave the EU and establish the future relationship between the UK and the EU”.
The critical legislation – known as the Withdrawal Agreement Bill – is expected to clear the Commons when MPs return from the Christmas recess, paving the way for the UK’s departure from the EU on 31 January.
However, Britain will then enter the transition period, remaining inside many of the bloc’s institutions and abiding by its rules until the future UK-EU relationship is negotiated between London and Brussels.
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Mr Johnson has consistently argued this can be delivered by December 2020, but Ursula von der Leyen, the new European Commission president, said an extension to the negotiating period may need to be agreed in the summer.
“I am very concerned about how little time we have,” she told the French newspaper Les Echos. “It seems to me that, on both sides, we should seriously consider whether the negotiations are feasible in such a short time.
Nigel Farage, the Brexit Party leader, urged Mr Johnson yesterday to walk away from talks with the EU if the prime minister is unable to secure favourable terms from Brussels by the end of 2020.
But he said he believed “some sort of deal will be cobbled together” and urged Brexiteers to be prepared to accept compromises on “all sorts”.
The Independent has contacted No 10 for comment.