Pollsters from Panelbase interviewed English voters to find out what price they would be willing to pay to see Brexit fulfilled.
A number of scenarios were put forward with people asked whether leaving the European Union would be worth it if it meant the UK lost Northern Ireland or Scotland or Gibraltar.
The 2016 referendum revealed stark differences in opinion between Scotland and England over the EU with 62 per cent of Scots voting to Remain in the organisation compared to 46.6 per cent south of the border.
In the survey voters expressed the most concern about Gibraltar leaving Britain, followed by Scotland, and were least worried about Northern Ireland going.
Over a third (37 per cent) said losing the British Overseas Territory on the southern tip of Spain would be too steep a price for Brexit, while 35 per cent said losing Scotland would not be worth it.
Only 31 per cent said the loss of Northern Ireland was not a price worth paying for Brexit.
Over 1,000 people were surveyed by the pollsters for the study commissioned by pro-independence website Wings Over Scotland. The sample included both leave and remain voters.
Meanwhile, across the whole of the British Isles enthusiasm for Brexit appears to be waning.
A UK-wide survey of more than 200,000 people found Britain would vote by a narrow margin to remain in the EU if another referendum were held next week, The Scotsman reported yesterday.
People in Scotland were most likely to say Britain would be economically better off inside Europe, at 63 per cent, including 13 per cent of Leave voters. They were also the most likely to say that Britain should stay in the single market, at 66 per cent.
Stephen Gethins MP, the SNP’s Europe spokesman, said the survey showed opposition to a “cliff edge” Brexit.
“This shows hardening opposition across Scotland to the Tories’ hard Brexit shambles, even among Leave voters,” Mr Gethins said.
“The UK government must listen and change course before they really take us to the cliff edge. ‘’They can no longer continue being deaf to the growing chorus of calls to protect jobs, investment and living standards – we should remain in the customs union and the European single market, which is around eight times bigger than the UK’s alone.
“Theresa May must stop pandering to the extreme Tory Brexiteers, whose agenda will do untold damage to the economy and jobs for many years to come.”