Theresa May has said she “sincerely hopes” Britain will leave the EU with a deal as Ireland’s Leo Varadkar made clear there was an “openness” to Brussels granting a short extension.

But as the Prime Minister arrived for the two-day European Council, Dalia Grybauskaite, Lithuania’s President, made clear there would be conditions attached to any extension of Article 50.

EU leaders are due to discuss Brexit this afternoon when Mrs May will address them. Brussels sources suggest that there is not yet unanimity on granting a short extension.

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The PM was due to have a bilateral meeting with Emmanuel Macron, the French President, who is said to be digging in his heels as he believes Brexit is delaying his plans for radically reforming the EU and needs to be brought to a conclusion.

Arriving in the Belgian capital for the EU summit, the PM said: "What is important is that Parliament delivers on the result of the referendum and that we deliver Brexit for the British people. I sincerely hope that we can do that with a deal.

"I am still working on ensuring Parliament can agree a deal so we can leave in an orderly way. What matters is that we deliver on the vote of the British people."

She added: "What matters is that we recognise that Brexit is the decision of the British people; we need to deliver on that. We're nearly three years on from the original vote; it is now the time for Parliament to decide.

"A short extension gives us that opportunity to decide to leave the European Union, to deliver on that result of that referendum and I sincerely hope that will be with a negotiated deal."

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Mark Rutte, the Dutch premier, said it was now up to Westminster to back Mrs May's deal, saying a no-deal Brexit would be "catastrophic" for the British economy.

"The ball has to be in the court of the British Parliament. They first have to say yes," he insisted.

"The signal today might be that if the British Parliament would say a yes, lock, stock and barrel, to everything on the table, then Europe understands that, technically, you need time to implement everything in law."

Speaking at an EPP meeting ahead of the EU summit, Mr Varadkar said there was an "openness to an extension" across the board among EU leaders.

He explained: "Everyone wants to avoid a no-deal but we can't have a situation whereby we have a rolling cliff-edge, where we just put off decisions and deadlines every couple of months.

"Brexit was never going to be clean. Brexit would always require some very hard choices for the United Kingdom to make. It was never going to be all good and no bad. And those decisions now need to be made."

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Asked whether he was in favour of a long extension, the Taoiseach said now was not the time to consider it.

He stressed Ireland did not want the UK to crash out of the EU and that it was up to the UK to revoke Article 50 if they chose to. "No-deal can only ever be a British choice," he declared.

"Let's not forget the March 29 deadline was set by the UK in the first place. It's always up to them, even at the last moment, to revoke Article 50 unilaterally.

"They do not need permission to do that so no-deal, if it happens, will be a British choice and a British decision."

Mr Varadkar added: "Brexit is not a problem of our creation. We do need to see resolution sooner rather than later. I don't think this can drag on for months and years."

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Meanwhile, Jeremy Corbyn has also been in Brussels for talks with Michel Barnier, the EU’s chief negotiator, and Martin Selmayr, Secretary General of the European Commission, which he said had been “very constructive”.

The Labour leader explained: "Our determination is to prevent a no-deal exit from the European Union next Friday. We are, therefore, looking for alternatives and building a majority in Parliament that can agree on a future constructive economic relationship with the European Union.

"We've been discussing how this could come about and trying to reach out here as both Keir [Starmer] and myself have been reaching out to colleagues in all parties in the UK Parliament."

Accompanied by Sir Keir, the Shadow Brexit Secretary, Mr Corbyn added: "This morning's meetings have been positive and we have done what I believe the Government ought to be doing - instead of bringing back a twice-rejected deal to the British Parliament - looking for constructive solutions."