An EU proposal for the Northern Ireland border threatens the “constitutional integrity” of the United Kingdom, Theresa May has said.
A draft legal agreement published by the EU proposes a “common regulatory area” on the island of Ireland after Brexit, if solutions cannot be found.
Mrs May said “no UK prime minister could ever agree” to this.
The EU says the controversial “backstop” option is not intended to “provoke” the UK.
Unveiling the draft agreement, EU chief negotiator Michel Barnier called on the UK to come up with alternatives.
He said the text was “no surprise” and was just a legally-worded assessment of what had been agreed so far.
Mr Barnier said the document contained “concrete and realistic solutions” in relation to the question of how to avoid a hard border once the UK leaves the EU’s customs union.
Other options – a UK-EU deal that means checks are not needed and technological solutions – will also be explored.
Speaking at Prime Minister’s Questions, Mrs May said she would be making her opposition to the “backstop” option “crystal clear” to the EU commission.
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Earlier the DUP’s Westminster leader Nigel Dodds said his reaction to the publication was one of “amazement” that the EU thought it “could possibly fly with either us or the British government”.
“We did not leave the European Union to oversee the breakup of the United Kingdom,” he told the BBC, adding that it would be “catastrophic” for Northern Ireland to be “cut off” from UK markets.
Conservative Brexiteers have also said it is “completely unacceptable” and would effectively annex Northern Ireland.
There is also opposition to any role for the European Court of Justice after Brexit – the EU is proposing that disputes over the Brexit agreement in future years be settled by a “joint committee” which can refer to the EU’s court for a binding decision.
According to the draft text, it would involve an “area without internal borders in which the free movement of goods is ensured”, covering customs, VAT, energy, agriculture, goods and other sectors.
The Irish government said this option was “very much a default and would only apply should it prove necessary”.
Ireland’s foreign affairs minister Simon Coveney said the publication was “another important step in the Brexit negotiations”.