This would include remaining in the customs union and single market.
The polling was conducted before Theresa May and the EU announced a breakthrough deal had been reached on the Ireland border issue, paving the way for talks to move on to the matter of future trade with the EU.
More than 2,000 people in Northern Ireland were asked whether they would vote to join a united Ireland or to stay in the UK "in the context of a 'Hard Brexit'... leaving the EU with no deal on the border, the Good Friday Agreement or citizens' rights".
The results showed 47.9 per cent of people would support joining the Republic of Ireland in the event of a hard Brexit, while 45.4 per cent would rather stay in the UK. Another 6 per cent said they were "undecided" but would definitely vote, while fewer than 1 per cent said they would not vote or spoil their ballot.
The poll also found 52.4 per cent of people believe there will be a reduction in rights because of exiting the EU and 75.8 per cent think EU standards should be maintained after leaving.
Speaking to the Derry Journal, Sinn Fein MEP Martina Anderson said the opinion poll results show “concern” about the “Tory/DUP Brexit agenda”.
“This vote, just like that of the majority who voted to remain in the EU in last year’s referendum, is drawn from all sections of society across the North,” she said.
“This shows the deep level of concern about the Tory/DUP Brexit agenda and reinforces that the DUP do not represent the views of the people of the people of the North.”
“While of course this is an opinion poll, it also chimes with what we have been hearing in our engagements with people from all sections of society from across the north,” she added.
“What this shows is that more and more people now realise that securing special status for the north within the EU is achievable and offers the best protection for the Good Friday Agreement and citizens rights.”
The poll was carried out by LucidTalk on behalf of the European United Left/Nordic Green Left (GUE/NGL) group in the European Parliament.
Concerns about the UK leaving the EU without a deal may have been somewhat allayed by the events of Monday morning. Standing alongside Ms May, European Commission president Jean-Claude Juncker said “sufficient progress” had been made on all three so-called “divorce” issues, including the Irish border.
The Prime Minister said there would be no hard border and the Good Friday Agreement would be upheld.
The Democratic Unionist Party said there was still “more work to be done” and suggested the party could still vote against the final deal.
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