The EU has once again ruled out renegotiating Theresa May’s Brexit deal, in a major blow to several Conservative leadership candidates who have insisted that they would re-open talks if elected.

Arriving at a summit in Brussels on Tuesday an exasperated Jean-Claude Juncker told reporters: “I was crystal clear. There will be no renegotiation.”

On the doorstep of the same meeting Theresa May also warned her potential successors against leaving the EU without a deal.

She told journalists she was “not going to comment on the views of individual candidates”, but added: “I continue to have the view that it’s best for the UK to leave with a deal.”

The summit, part of the process of appointing Mr Juncker’s successor, will be one of the last meetings the lame duck prime minister attends in the EU capital, with the final one currently scheduled for June during the Tory leadership contest.

A new Commission president is expected to be in post after 31 October, which is also the current Brexit deadline – meaning whoever replaces Ms May will have to deal with Mr Juncker to avoid a no-deal.

But none of his possible replacements have massively different views on Brexit, and the direction of policy on the issue is in any case set by member states.

The level of continuity Brexiteers can expect from Brussels is epitomised in the fact that one of the candidates to replace Mr Juncker is in fact Michel Barnier himself, the EU’s chief negotiator.

Brexiteer such as Dominic Raab and Boris Johnson who want to lead the party have said they would be open to leaving without a deal – a course of action expected to bring about economic chaos for the UK.

The EU has repeatedly said for months that it will not renegotiate the withdrawal agreement with the UK, and that it is the only deal on the table, though it is open to changes to a separate document – the political declaration for the future relationship – which spells out the future trading arrangements.

Theresa May warns against no-deal Brexit

But Ms May has repeatedly failed to get MPs to approve the deal. A fourth attempt to bring the withdrawal agreement before the House of Commons set in motion a chain of events that led to the prime minister announcing her resignation on Friday last week.

Tuesday European Council meeting, attended by all 28 EU leaders, is one of the first in the EU capital for some time where Brexit has not been discussed in at least some capacity.

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The prime minister appeared in good spirits as she arrived at the meeting, as if a weight had been lifted from her shoulders. Explaining her attendance despite her lame duck status and Britain's departure, she said:

"While we're still a member of the European Union, while I am prime minister, I'll be continuing to meet the obligations of the office and the duties of the office.