The gap between the Yes and No camps is down to nine points, with the independence campaign on 38 points, while the pro-Union side is on 47 per cent, according to the poll by Survation. The narrowing gap is down from 20 points in a survey by the same pollster last month.
It is the first survey of opinion since Chancellor George Osborne, along with Labour and the Liberal Democrats, warned that Scotland could not share sterling after a Yes vote in the referendum.
Support for Yes has been edging up since the turn of the year and the latest survey represents another rise.
The poll of 1,005 Scots also found that 65 per cent wanted to see the SNP government set out a Plan B on currency if the Westminster parties do not climb down after a Yes vote.
More than a third (37 per cent) of pro-independence supporters want to see Scotland have its own separate currency.
Deputy First Minister Nicola Sturgeon said the poll is “exceptionally encouraging” for the Yes campaign.
“It is clear that there has been a severe backlash to George Osborne’s bluster and threats on the pound – with more than half of the No campaign’s lead wiped out in just three weeks,” she said.
“Far more people are more likely to vote Yes on the back of the Westminster establishment’s attempted bullying rather than No.”
But Alistair Darling, head of the pro-union Better Together campaign, said the SNP must set out a currency Plan B.
He said: “We know that if we leave the UK, we are leaving behind the security of the pound.
“Scots are clearly saying to Alex Salmond that he cannot keep us in the dark.”
Polling expert Professor John Curtice of Strathclyde University said the poll showed no sign of a boost for the Better Together campaign in light of the currency row.
He said: “When one looks at this poll, one has, at minimum, to conclude that it offers no evidence that the currency intervention has delivered the No side any immediate boost.”
The poll showed that just 37 per cent believe Westminster is not bluffing while more than half (52 per cent) think that a currency union would be in the interests of the rest of the UK.
Better Together has written to households across Scotland spelling out what losing the pound would mean for families.
Joanne Piercy, a working mother of three, says in the letter on behalf of the campaign that “losing the pound means bigger risks for us all”.
“The news that voting to leave the United Kingdom will mean Scotland would lose the pound has made my mind up,” Ms Piercy’s letter adds.
“I’ll be voting No in September because Scotland staying in the UK means more security for my family.”
Alex Salmond came under pressure at First Ministers’ Questions yesterday to make a statement to parliament on currency, setting out the Scottish Government’s alternative to keeping the pound.
Liberal Democrat leader Willie Rennie said: “Despite all the opinion, including on his side, he can’t even say that it might be a possibility, and he can’t hide on that until September.
“It will be the Chancellor after a Yes vote, if that were to happen, whom he will have to convince about a currency union.
“The First Minister’s whole plan is based on the judgment of that Chancellor, George Osborne. And this is a man he derides for his judgment every day of the week.”
The poll also shows the SNP is 13 points clear of Labour in voting intentions for the Holyrood elections in 2016. The Nationalists are on 44 per cent compared with Labour on 31 per cent. The Tories are on 13 per cent, with the Liberal Democrats struggling on 6 per cent, according to the survey.
Ms Sturgeon added: “The remarkable level of support for the SNP after nearly seven years in government – with comparable levels of support as our 2011 election landslide – is a real vote of confidence in the SNP government’s strong record of delivering for people in Scotland.”