The anti-Brussels MEP also said EU chief Martin Schulz had confirmed to him that as Scotland had entered the bloc as part of the UK, it also had to leave as part of the UK.
Mr Coburn declared: “When Nicola Sturgeon had her summit with President Schulz I decided I would have a summit with President Schulz.
“I went and had a chat with him and he said we cannot remain in the European Union.
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David Coburn insisted Scotland had subsequently voted to leave the European Union
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“Scotland entered into the European Union as part of the UK, it must leave as part of the UK and then reapply. [Scotland] will have to reapply after Turkey.”
Bashing the possibility of Scotland reapplying for EU membership after the UK leaves the bloc, Mr Coburn suggested it was unsustainable as the country would have to accept the euro.
“There is no central bank, we will have to accept the euro which is a catastrophe,” the Ukip MEP continued.
“One or more countries are probably going to crash out of the euro in the next year or so, the euro is very unstable.
Nicola Sturgeon has repeatedly threatened to hold a second vote on Scottish independence
[President Shultz] said we cannot remain in the European Union
“We would have to accept the euro, we would have to have an international border 50 miles from Edinburgh that is not a good idea.
“We do four times as much business with the rest of the UK, England than we do with the European Union.”
He added: "We have to leave, there is no other way.
"We decided in the referendum on Scottish independence to remain British, we then subsequently decided to [we do not] want to be in the European Union.”
Theresa May's 12 point Brexit plan Mon, January 16, 2017
It's finally here!
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Continued cooperation with the EU to tackle terrorism and international crime.
Mr Coburn’s demand for "Remoaners" in Scotland to get behind the EU referendum result comes as a poll showed more than half of Scots do not want another independence vote in the next few years.
Earlier this month, the SNP once again threatened to hold a second vote on Scottish independence after Mrs May indicated she would reject SNP demands for a bespoke Brexit deal.
However, the Panelbase survey of 1,020 voters for the Sunday Times found 51 per cent of those surveyed were not supportive of a second referendum within the next year or two.
Despite the findings, Ms Sturgeon's predecessor, Alex Salmond, argued a new vote should be held within a year or two if the Prime Minister "bulldozes" her way to a Brexit deal which hurts jobs and investment in Scotland.
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