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Britain and the EU agreed Thursday to hold more talks to try to avoid a no-deal Brexit, after a "robust" meeting between Prime Minister Theresa May and European Commission chief Jean-Claude Juncker.

A joint statement issued after the talks in Brussels said Juncker had again warned that November's withdrawal agreement could not be renegotiated - after May came hoping to persuade Brussels to change the so-called "backstop" clause for the Irish border.

But Juncker expressed only his "openness to add wording" to a parallel political declaration laying out ambitions for future EU-UK ties if London wants to seek a "more ambitious" closer relationship after Brexit.

After his own talks with May, EU President Donald Tusk warned there was "no breakthrough in sight", though the British leader said she had seen willingness from Brussels to find a deal.

"Prime Minister May did not offer any new concrete proposals on the way forward," an EU official told AFP after May's meeting with Tusk.

Talk has been growing that Britain may have to delay Brexit to give enough time to get the necessary legislation through parliament, but May vowed once again to bring Britain out of the bloc on schedule on March 29.

"I'm going to deliver Brexit, I'm going to deliver it on time. That's what I'm going to do for the British public. I'll be negotiating hard in the coming days to do just that," she said.

The EU official said Tusk had asked May about the timeline for British officials and parliament to ratify and implement a deal, but received "no clear answers."

And Tusk also, the official said, suggested to May that she study a Brexit plan laid out earlier in the day by British opposition Labour leader Jeremy Corbyn, which "might be a promising way out of the impasse." May did not respond.

Legally-binding changes

In a sharp reminder of the urgency of finding a solution before Brexit day, Bank of England governor Mark Carney warned that Britain's economy was "not yet prepared" for a no-deal departure.

May said she had spelled out to Juncker and Tusk Britain's "clear position" that legally-binding changes are needed to the backstop to win round MPs fearful it could be used to "trap" Britain in the bloc against its will.

Such changes were not forthcoming, but instead she got a fresh round of talks.

EU negotiator Michel Barnier will now meet British Brexit Minister Stephen Barclay in Strasbourg on Monday, but an EU official described these as "exploratory talks," adding: "There is no mandate to negotiate."

May herself will meet Juncker again before the end of February, a commission spokesman said.

Expectations for Thursday's visit were already modest when, a day earlier, Tusk and Juncker torched May's prospects of winning changes to the withdrawal agreement.

Juncker told reporters May knows and accepts the Union will not reopen talks on the deal, while Tusk, who represents EU member governments as head of the European Council, triggered outrage across the Channel by damning pro-Brexit politicians for - in his view - recklessly failing to plan.

"I've been wondering what that special place in hell looks like, for those who promoted Brexit without even a sketch of a plan how to carry it out safely," Tusk said.

May said she had raised the incendiary remarks with Tusk, calling them "not helpful" and saying they had caused "widespread dismay" in Britain.

'Don't gamble with peace'

Ahead of the trip, Number 10 said that because the British parliament rejected the deal, May must seek material changes to the accord or see it fail.

The impasse in Brussels has deepened fears that Britain could crash out of the EU without a deal on March 29, disrupting trade and supplies to manufacturing.

May has exasperated EU leaders by repeatedly coming to Brussels without detailed proposals to solve the Brexit deadlock, and Tusk warned her he expected her to bring "a realistic suggestion on how to end the impasse".

Corbyn, the leader of the main opposition Labour party, wrote to May on Thursday setting out his five conditions for backing her on Brexit - including the UK staying in the EU's customs union.

While his demands will not be palatable to many in May's Conservative party - not least because of the deeply-entrenched tribalism of British politics - it suggests there may be room for manoeuvre, if not yet a clear path to a cross-party deal.

The EU official told AFP that Brussels has not had long to study Corbyn's plan, but that Tusk had recommended May look it over.

May will have dinner with her Irish counterpart Leo Varadkar in Dublin on Friday.

Painstaking talks

Varadkar, whose government has stressed the importance of maintaining an open border between Ireland and Northern Ireland after Brexit, said recent "instability in British politics" showed why a backstop was essential.

Last month, the House of Commons overwhelmingly rejected the Brexit deal that May had negotiated with the EU after 18 months of painstaking diplomacy.

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