A ComRes survey for ITV Border News of voters in Dumfries and Galloway and the Scottish Borders council areas in June found 61% propose to vote No, up from 59% in January.
There was also a similar rise in support for independence, with this increasing from 24% to 26%, according to the poll, which was carried out for ITV Border’s political programme Representing Border.
Meanwhile, 13% of people said they were undecided about how to cast their ballot, compared to 17% in January.
When those who do not know how they are going to vote are excluded, 70% of people polled are in favour of Scotland staying in the UK, while 30% want to end the Union.
Better Together campaign director Blair McDougall said: “With less than 100 days until we make the biggest decision in our history, it is encouraging that our campaign speaks for the overwhelming majority of people living in the south of Scotland.
“Earlier this week Alex Salmond claimed his campaign was winning the referendum, yet this poll proves the nationalists’ campaign is failing badly.”
He added: “We offer a vision of Scotland that we can all unite around. We can have the best of both worlds for Scotland. We can have our strong Scottish Parliament, with the guarantee of more powers for Scotland, backed up by the strength, security and stability of being part of the larger UK. Only separation puts that at risk.
“Whilst it is encouraging that we speak for the majority of Scots, there can be no complacency. We will be working hard every day to convince people to say No Thanks to separation.”
Increase in Yes Backing
Blair Jenkins, the chief executive of the pro-independence Yes Scotland campaign, said: “Three other polls in recent days have recorded a significant increase in backing for Yes, with average national support for independence at 47% - putting us in touching distance of success in September. One poll recorded support for Yes at 48% - a campaign high.”
He added: “With a Yes vote, the south of Scotland will have an eighth of the members of an independent Scottish Parliament - a huge increase on just 1% of Westminster parliamentarians.
“We are increasing our vote in the Borders, and with three months to go we’ll continue to work for every single vote by showing that only a Yes can safeguard the gains of devolution, which are seen perhaps most clearly in the Borders - including free bus passes, free care for the elderly and no prescription charges. And with a Yes vote we can extend these gains to other areas of policy currently controlled by Westminster.”