THERESA May today love-bombed Ireland in a last-ditch bid to convince them to fix the Brexit backstop.
Speaking in Belfast, the PM vowed to back a joint bid for the 2030 World Cup by all the countries of the British Isles.
And she pledged that after Brexit, the UK will have a closer relationship with Ireland than with any other European country.
Mrs May also risked angering her MPs by suggesting she might not ditch the backstop after all.
In a speech aimed squarely at winning goodwill from Dublin, the PM said: "Our relationship with Ireland is deeper than our relationship with any of the other 27. It is uniquely rooted in ties of family, history and geography.
"The recent past has been a moment of reflection in the UK and Ireland as we have commemorated the centenary of a series of key events in our shared history.
"Today those ties of family and friendship between our countries are more important than they have ever been.
"And I believe there is a yearning in the hearts of all the peoples of these islands for a close and trusting relationship between all of us, and an absolute horror that we should take even a single step backwards in the progress we have collectively achieved."
There is a yearning in the hearts of all the peoples of these islands for a close and trusting relationship
Theresa May
She proposed annual meetings between the British and Irish governments after Brexit to ensure the two countries work closely together.
And she added: "Both the UK and the Irish Governments have already made clear that we would support the tantalising possibility of a joint UK and Ireland World Cup bid for 2030, should our respective football associations choose to pursue this."
Mrs May admitted she must "face up" to the fact that MPs resoundingly rejected the Irish backstop plan - which could leave the UK trapped in the European customs union.
But she hinted she may not ditch the backstop altogether, saying that any Brexit deal will need "an insurance policy for the future".
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Earlier today DUP leader Arlene Foster vowed to back the PM's deal if she succeeds in rewriting the plan for the Irish border.
The DUP are crucial to Mrs May's strategy - because she believes if they come on board and back her deal, dozens of Tory Brexiteers will follow.
Today Mrs Foster told the BBC: "If the backstop is dealt with in the withdrawal agreement, then despite the fact that we may have misgivings around other parts of the agreement, we will support the Prime Minister.
"Because we do want Brexit to happen in an orderly fashion."
The unionist boss said the "current backstop" would have to be replaced by a different way of keeping the Irish border open.
She promised to lobby Mrs May on the issue when they hold talks in Belfast tomorrow.
She said: "We will be reiterating our opposition to the current backstop. And the fact that Parliament has now backed that position means that she has a clear mandate to go back to Brussels.
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"The current backstop is toxic to those of us living in Northern Ireland, and indeed for unionists right across the United Kingdom, because it would cause the break-up of the United Kingdom into the medium and longer term."
Mrs May got a boost from Angela Merkel yesterday as the German leader called on Brussels to be flexible with Britain.
And a grand committee of Tory MPs from across the Brexit divide is meeting civil servants for a second day of talks on how to find "alternative arrangements" which could replace the backstop.
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