Theresa May has said her Brexit deal is “the only deal available” and that the controversial Northern Ireland backstop is “necessary” after being rebuffed in a meeting with Angela Merkel and other EU leaders on Tuesday.

The prime minister has been criss-crossing Europe in a bid to win concessions from the EU after she was forced to pull a Commons vote on the plan at the last minute this week.

Speaking in Brussels ahead of a meeting with EU president Jean-Claude Juncker Ms May echoed EU language and said the agreement was “the best deal available, indeed it’s the only deal available”.

She added: “The backstop, which is the issue that parliament has raised, the backstop is a necessary guarantee for the people of Northern Ireland and whatever outcome you want, whatever relationship you want in the future, there is no deal available that doesn’t have a backstop in it.”

The admission brings the prime minister into line with the EU’s view, but could further enrage Eurosceptic rebels in her own party, some of whom want to oust her over the plan.

Mr Juncker had said this morning that there was “no room whatsoever for renegotiation” and that the re-opening of the withdrawal agreement “will not happen”.

The prime minister also met with Dutch PM Mark Rutte in the morning and will be meeting Irish leader Leo Varadkar on Wednesday. She will return to Brussels on Thursday and Friday to attend a meeting of the European Council, which all 28 EU leaders will attend.

After meeting with Ms May, the German chancellor Angela Merkel said there was “no way to change” the agreement, echoing the sentiments of other member states.

Speaking separately in Brussels, French European affairs minister Nathalie Loiseau told reporters: “We’ve done a lot to help the UK, this withdrawal agreement is the only possible agreement, and we’ve done a lot of concessions to reach it. We sincerely hope that there can be a majority to ratify the withdrawal agreement but we have to stand ready for a no deal and we are preparing for it.”

European Council president Donald Tusk, who met with Ms May in Brussels separately to Mr Juncker, said he and the prime minister had had a “long and frank discussion”. He added that it was “clear that the EU27 wants to help” but that “the question is how”. Ms May said she believed there was “a shared determination to deal with this issue and address this problem”.

Though EU leaders and governments have said they will not renegotiate the deal, some have said they would like to help Ms May pass the plan through parliament by providing “reassurances” and “clarification”.

Ms May appeared happy with this, telling reporters in Brussels: “We don’t want the backstop to be used and if it is we want to be certain that it is only temporary. It is those assurances that I will be seeking from fellow leaders over the coming days.”

Tory Eurosceptic rebels and the DUP have made clear that the backstop would have to be removed from the deal, time-limited, or the UK given the power to end it unilaterally if they are to back it. Without their support Ms May has little chance of passing the deal.

Her admission that she is unlikely to be able to secure substantial changes to the agreement is likely to enrage Eurosceptics, amid reports from Westminster that a no-confidence vote from her own party could be looming.

Theresa May and Jean-Claude Juncker meet in Brussels on Tuesday evening (Reuters) (REUTERS)

Speaking in the European Parliament in Strasbourg in the morning, commission president Mr Juncker said: “The backstop is necessary for Ireland. Ireland will never be left alone.”

He described Brexit as “a surprise guest” at the European Council summit scheduled for this end of this week, adding: “I am surprised because we had reached an agreement on 25 November together with the government of the UK.”

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“The deal we have achieved is the best deal possible, it is the only deal possible, and so there is no room whatsoever for renegotiation,” he said.

“There is room enough to give further clarity and further interpretations without reopening the withdrawal agreement.