THORNTON MANOR, England - Prime Minister Boris Johnson met his Irish counterpart in northern England on Thursday in a last-ditch attempt to revive a British proposal for a Brexit deal that the European Union said falls far short of what is needed for an orderly departure.

Ireland is crucial to any Brexit solution. The EU member must approve any plan for its border with the British province of Northern Ireland, the bloc's only land frontier with the United Kingdom.

But with just three weeks before the United Kingdom is due to leave the world's biggest trading bloc, no solution has been found to avoid reimposing a hard border, making it unclear on what terms it will quit or even whether it will at all.

As both sides position for another delay followed by a British election, or an acrimonious divorce on Oct. 31, Johnson met Irish Prime Minister Leo Varadkar at Thornton Manor in Cheshire on Thursday.

"Looking forward to a detailed discussion to see if we can make any progress," Varadkar said on Twitter. He posted pictures of the two leaders smiling and shaking hands. Johnson posted a picture of the two leaders shaking hands.

Johnson said on Wednesday that he was cautiously optimistic, though Varadkar said on Tuesday that it would be very difficult to strike a Brexit deal by next week - when the EU holds a crucial summit on Thursday and Friday.

EU diplomats, though, are sceptical about the chances of a deal. Most expect Johnson to be forced to accept a delay to Brexit - a step that could ultimately lead to either a disorderly exit or the reversal of the entire Brexit endeavour.

BLAME GAME

Brexit descended into a public row between London and Brussels this week after a Downing Street source said a Brexit deal was essentially impossible because German Chancellor Angela Merkel had made unacceptable demands.

The EU accused Johnson of playing a "stupid blame game" and bluntly told London on Wednesday - exactly a week since Johnson's initial bid for a last-minute deal - that it would have to make further significant concessions.

Former British foreign minister Jeremy Hunt said on Thursday that a "catastrophic failure in statecraft" could lead to a no-deal Brexit as Johnson would likely win an election and, then emboldened, be unwilling to compromise.

Hunt said the EU was misreading British domestic politics as it had when dealing with both former prime ministers David Cameron and Theresa May.

"If Boris wins, which is what the polls are saying, at the moment, and he comes back with a majority, that British government will be much less willing to compromise," Hunt told the BBC.

Though Ireland is only about an eighth of the size of the United Kingdom's $2.8 trillion economy, Dublin is backed by the rest of the EU whose economy - minus the United Kingdom - is worth $15.9 trillion.

While Ireland would be very badly affected by a no-deal Brexit, the relative importance of Ireland in the negotiations up-ends centuries of history in which it has had a much weaker hand than London, both before and after winning independence from Britain.

The EU's two most powerful leaders, Germany's Merkel and French President Emmanuel Macron, will meet at the Elysee Palace on Sunday ahead of next week's summit.

"We want to reduce the negative effects, even if there is a disorderly Brexit, in both countries," Merkel said.

(Writing by Guy Faulconbridge; editing by Alistair Smout and Angus MacSwan) ((guy.faulconbridge@thomsonreuters.com; 07825218698;))