A majority of British voters would choose leaving the EU Customs union over avoiding a hard border in Ireland.
The research, undertaken by former UK Conservative Party deputy chairman Michael Ashcroft found that 41% would accept a hard border if it allowed the UK to leave customs union.
Just 32% said they would choose to avoid a hard border - with 27% undecided.
Amongst those who voted to leave the EU, two thirds would prefer to leave the customs union than avoid a hard border.
55% of 'Remain' voters on the other hand, would make the opposite choice.
However, only one third of British voters share the view that it would be unacceptable for the region to be treated differently to the rest of the UK after Brexit
Some 30% said a special status arrangement for Northern Ireland would be acceptable as part of a deal to reach a sensible Brexit deal, while 14% said it would be "perfectly acceptable."
More than one-in-five said they did not know.
63% of 'Leave' voters said they would still choose to leave the EU if it resulted in the break-up of the UK.
In more general terms, just over half of British voters said they did not have a view on whether Northern Ireland should remain a part of the UK, answering "It is for the people of Northern Ireland to decide."
Of those, 69% said they would be happy to see Northern Ireland leave, or would not mind either way.
More than half of British voters (55%) said they believe the border issue is being “deliberately exaggerated by politicians and others to suit their own political agenda.”
Some 52% said they believe modern technology would allow border checks to happen "quickly and easily, so a border would not be damaging or disruptive."
However, nearly two-thirds of voters in northern Ireland agreed that a hard border would be “likely to provoke paramilitary activity and threaten peace and security” in Ireland.
85% of voters in the Republic of Ireland agreed.
Just over a third of voters in the Republic of Ireland said they would like to see a united Ireland in the next few years.
A majority said they were in favour of a united Ireland in principle, but said it "would not be practical or affordable for the Republic of Ireland in the next few years.”
More than 80% of nationalists and 30% of unionists said they believe there will be a 'border poll' on Irish reunification within the next ten years.
Some 49% of northern voters said they would vote to stay in the UK in any border poll, 44% said they would vote to leave, and 7% said they did not know.