The DUP has dismissed an opinion poll which shows that a majority of Remainers and Leavers in Great Britain would be prepared to abandon Northern Ireland in order to secure their preferred Brexit outcome.
Four in 10 of those taking part in the YouGov poll said they cared little, or not at all, about Northern Ireland.
A DUP spokesperson said: "The poll that matters is on December 12 when unionists can send a strong team of DUP MPs to Westminster who will speak up for Northern Ireland and strengthen our place in the United Kingdom."
But the SDLP said the opinion poll was significant. West Tyrone MLA Daniel McCrossan said: "Brexit has shifted the constitutional plates across these islands.
"People across all communities are questioning where their interests are best served and what kind of future they see for themselves and their family.
"That's a conversation that we welcome and we're very clear, the interests of people, business and communities here are best served in the European Union."
Alliance deputy leader Stephen Farry said: "The marginal interest in Northern Ireland is alarming but it shouldn't be surprising.
"There are responsibilities for both the UK and Irish governments regarding Northern Ireland, which neither can dismiss.
"Ultimately, the lesson we all need to take from these surveys is the people and politicians of Northern Ireland need to work together to overcome our differences and make this society a success for everyone."
A total of 41% of those taking part in the YouGov poll said they cared little or not at all about Northern Ireland.
A majority would rather have their preferred Brexit outcome than see Northern Ireland stay in the Union, which was true for both Remainers and Leavers.
The research found that even those who care a "great deal" about Northern Ireland, and want it to stay in the UK, would choose their Brexit preference over the Union remaining intact.
A total of 1,641 adults in Britain were asked about the issue between October 23 and 24.
YouGov said: "New YouGov polling today exposes the weaknesses in the link between Northern Ireland and the rest of the UK.
"YouGov asked mainland Britons how much they care about Northern Ireland, how they'd feel if it left the Union and whether getting their own way on Brexit was more important than keeping the UK together."
The polling organisation said its results showed that 41% said they "would not be bothered" if Northern Ireland left the UK.
A further 41% said they would be "upset" if Northern Ireland broke away, while only a minority of 9% would be "actively pleased to see them go".
The referendum divide did not make a difference, with 58% of Remain voters and 64% of Leave voters saying they'd rather have their own way on Brexit than see the Union preserved.
YouGov added: "As with so much, however, Brexit takes precedent. Given the choice between having their preferred outcome on Brexit and Northern Ireland staying in the Union, a majority of 58% chose the former and only 18% the latter."
The Irish border has been one of the key sticking points in the Brexit negotiations between the UK and EU.
The polling organisation added: "Even those Britons who say they want Northern Ireland to stay part of the UK tend to be willing to sacrifice it for the sake of Brexit.
"Almost half (47%) chose their preferred Brexit option, compared to 35% who chose the Union."