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Leading Conservative Brexiteer Jacob Rees-Mogg said it was wrong to involve Charles in the "immediate political controversy" on the day the Prime Minister signed a new agreement with her.

Baroness Arlene Foster, the former Democratic Unionist Party (DUP) leader and first minister of Northern Ireland, said the meeting in Windsor Castle was "crass and will go down very badly".

Buckingham Palace said Charles was acting on "the Government's advice". Downing Street said it was "fundamentally" a decision for the King.

Charles welcomed Ms von der Leyen to Windsor Castle at the end of her busy day following a joint press conference with Mr Sunak to outline the new deal dubbed the "Windsor Framework".

The briefing for the major political development, which in some ways aims to heal tensions between the UK and EU, was staged at Windsor Guildhall where the King and the Queen Consort married in 2005, a ceremony that set the seal on their long relationship.

Charles was pictured warmly shaking hands with the EU chief in a drawing room of the royal residence where they were served tea during their discussions said to be very productive.

Topics covered included climate change and the Russian invasion of Ukraine, but it is not known if Northern Ireland was on the agenda.

There have been reports suggesting the meeting was arranged following a direct approach by the EU chief to Buckingham Palace, but this would be highly unusual as the normal channels of communication would go through the UK Government.

A Buckingham Palace spokesman said: "The King is pleased to meet any world leader if they are visiting Britain and it is the Government's advice that he should do so."

But ahead of the King's audience with Ms von der Leyen, Mr Rees-Mogg, a former Cabinet minister, said: "It is surprising that The King will meet Ursula von der Leyen today as it antagonises the people the Prime Minister needs to conciliate.

"It is also constitutionally unwise to involve the King in a matter of immediate political controversy."

Baroness Foster added: "I cannot quite believe that No 10 would ask HM the King to become involved in the finalising of a deal as controversial as this one. It's crass and will go down very badly in NI.

"We must remember this is not the King's decision but the Government who it appears are tone deaf."

There had been warnings the meeting could draw the King, who as head of state must remain politically neutral, into the process of the UK and EU agreeing a deal or be seen as tacitly endorsing it.

Before the King and EU chief met, Downing Street defended the move to advise the King to meet Ms von der Leyen, saying Mr Sunak "fundamentally" believed the final decision was for Charles.

"He firmly believes it's for the King to make those decisions," the Prime Minister's official spokesman said.

He compared the von der Leyen meeting to Charles talking to Poland's Andrzej Duda or Ukraine's President Volodymyr Zelensky.

Asked why the final protocol talks were taking place in Windsor, he said: "There are a number of occasions when these sorts of talks have been held in significant locations, this is no different."

Conservatives were among those voicing their criticism of the meeting before it was even confirmed, following suggestions the deal would be called the "Windsor Agreement".

And Sammy Wilson, the DUP's chief whip said the expected meeting would risk dragging the King into a hugely controversial political issue".

Royal commentator Peter Hunt, tweeted about the King: "He's abandoned his unifying role and entered the political fray, in a foolish bid to be seen as statesmanlike.

"History won't be kind. Someone's head will roll."

European Commission deputy chief spokeswoman Dana Spinant insisted the meeting was "not part of this process" to secure a deal.

Windsor Framework: King Charles criticised for ‘constitutionally unwise’ tea with EU chief Ursula von der Leyen