EVERYONE in the EU is “in trouble” if the new British Prime Minister wants to tear up the Withdrawal Agreement, Ireland's deputy premier has warned.

Simon Coveney said that a no-deal outcome would be a British choice, not an Irish or an EU one and, in such circumstances, the future relationship with the EU could be changed.

He also reiterated that Ireland would have to carry out checks in the event of a no-deal Brexit but those checks would not be at the border between Northern Ireland and the Republic.

"If the approach of the new British Prime Minister is that they're going to tear up the Withdrawal Agreement, then we're in trouble, we're all in trouble, quite frankly, because it's a little bit like saying: 'Either give me what I want or I'm going to burn the house down for everybody'," Mr Coveney told the BBC's Andrew Marr on Sunday.

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But he stressed: "The EU has made it very clear that we want to engage with a new British prime minister, we want to avoid a no-deal Brexit."

Mr Coveney maintained the backstop could be avoided by negotiation but that it still needed to be part of the Withdrawal Agreement; which has been repeatedly rejected by the UK Parliament.

"The idea that we can consider moving away from something that took two-and-a-half years to negotiate given all of that complexity and compromise on both sides to try and accommodate British redlines, don't forget, not EU redlines, we're simply not going to move away from the Withdrawal Agreement," declared the Tanaiste.

The Cork politician denied that a no-deal was where the situation was headed.

He said it would only happen if MPs enabled it to happen, explaining: "If the House of Commons chooses to facilitate a no-deal Brexit and if a new prime minister chooses to take Britain in that direction then it will happen but this is a British choice, not an Irish choice, not an EU choice, this is a British choice.

"We all want to avoid a no-deal Brexit...We want to try to resolve these issues but we won't do it on the basis of being told what will happen."

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Ireland’s Deputy PM reiterated that checks would have to be carried out on the island of Ireland in the event of a no-deal Brexit but he said those checks would not be at the border.

"We have to protect relationships and peace on the island of Ireland, and we are not going to create a security risk by putting a border in place on the border, but we also have to make sure that there are verification mechanisms to ensure what the EU knows what is coming into its single market," he said.

He added: "There will need to be checks somewhere. We are working out with the European Commission how that will work."

But he said such a scenario would "fundamentally disrupt" the all-island economy.

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Writing in the London edition of The Sunday Times, Mr Coveney warned that a no-deal Brexit would "devastate" Northern Ireland's economy.

"If Britain decides to leave without a deal, it would cause huge damage to us all," he insisted but noted how Northern Ireland would be the hardest hit in such a scenario.

"A no-deal Brexit will devastate the Northern Irish economy with tariffs and rules that will fundamentally disrupt the all-island economy upon which so much progress has been built,” added Mr Coveney.