Dr Elaine Murray was asked about having two borders to contend with in the event of Scottish Independence leading to the country rejoining the EU – one with England and one with Northern Ireland.
And she said: “The east of Dumfries and Galloway is very closely tied to Cumbria, and Carlisle in particular, and there are some people who live in Carlisle and work in Dumfries and Galloway too.
“We have a lot of people who work either side of the Border, it would be very serious indeed, both economically and in terms of people’s lifestyle here.
“It’s very important for us to have an open border, but also for our visitors. In terms of tourism to the region, a lot come from the north of England.”
She added: “I would also be very concerned about the border to the west of Dumfries and Galloway, with Northern Ireland.
“If it was the case that Scotland was independent and Northern Ireland remained a part of the UK that would be a big problem for us.
“It’s a major route for freight, especially animals, as part of the agriculture industry.”
Shona Haslam, the Conservative leader of Scottish Borders Council, echoed Cllr Murray’s sentiments and said: “When you live here you realise there is no border here. People here don’t see the border, and they certainly don’t pay attention to it. I think people are living in cloud cuckoo land if they think Scotland becoming independent is an easy, straightforward process.
“It’s a very glib statement to make when there are so many economic, cultural and infrastructure links across the communities in the borders, which are reliant on each other.”
In response, depute leader of the SNP Keith Brown said: “The overwhelming majority of people in Scotland oppose Brexit.
“And we believe that the best way to build a more prosperous and equal Scotland is to be a full independent member of the EU.”
An SNP spokesperson added: “The Scottish Government has no plans to close the border either now or post independence.”