The latest TNS survey reveals that 28 per cent of people who backed Labour in the 2011 Holyrood election plan to vote Yes in September's referendum, excluding those who are unsure. The figure is up from 21 per cent, on average, over the previous three months, when Labour "don't-knows" are stripped out.
TNS's findings also suggest the race is becoming closer after a period when the Yes campaign failed to eat into the No camp's lead. The poll put No on 56 per cent and Yes on 44 per cent, when the don't-knows were excluded.
Yes Scotland chief executive Blair Jenkins said it was an extremely encouraging poll but Better Together insisted it showed the majority of Scots want to remain as part of the UK.
Looking at all Labour supporters, including don't-knows, TNS found 58 per cent in favour of No, 22 per cent for Yes and 21 per cent undecided.
But the news that a growing number of Labour voters intend to back independence came as Peter Kilfoyle, the former Labour MP for Liverpool Walton, publicly backed a Yes vote, timing his announcement to coincide with a visit to the city by First Minister Alex Salmond.
The drift to Yes will come as a major blow to the No campaign.
Labour voters, many of whom are swithering over independence, have been carefully targeted by the SNP, which knows their support is vital if the referendum is to deliver a Yes vote.
In a party conference speech earlier this year, Deputy First Minister Nicola Sturgeon claimed independence would allow Labour supporters to reclaim their party.
Labour leader Ed Miliband visited Scotland at the end of last month in a bid to shore up support for a No vote in his party's traditional heartlands. In a keynote speech, he said his priority was tackling low pay and inequality, which he sought to contrast with SNP plans to cut corporation tax for big business and maintain a lower top rate of income tax than Labour for higher earners. The visit was part of a major effort by Labour to step up its referendum campaigning.
Former Prime Minister Gordon Brown has been put at the heart of the party's "United with Labour" campaign. Meanwhile, deputy Scottish Labour leader Anas Sarwar has taken a battle bus across the country and Shadow International Development Secretary Jim Murphy has undertaken a 100-town tour on behalf of the cross-party Better Together campaign.
Drew Smith, Scottish Labour's constitutional spokesman, said the party would continue to push a message of "partnership and co-operation with our neighbours".
He added: "We believe the majority of Scots, whatever their previous voting habits, recognise that a proud No vote will give Scotland the best of both worlds - more powers guaranteed for the Scottish Parliament but backed by the strength and security of the United Kingdom.
"The SNP have failed to make the argument for breaking up the United Kingdom and the separatists' case is being overwhelmingly rejected by the majority of the Labour movement."
The survey of 995 voters was conducted between June 25 and July 9. It compared with the previous TNS poll, for the Hunter Foundation, which had No on 59 per cent and Yes on 41 per cent. Using those figures, the No campaign's lead has shrunk from 18 points to 12.
Including the don't-knows, TNS found 41 per cent backing No, 32 per cent backing Yes and 27 per cent unsure. No was down one point on the previous directly comparable poll in May, while Yes support was unchanged.
The nine-point lead for No is down from 19 points last September, when the series of TNS polls began.
Mr Jenkins said: "This is an extremely encouraging poll. It's the highest level of support for Yes so far in a TNS referendum poll, and the No lead has more than halved since last September. Among those who are certain to vote, 45 per cent already plan to vote Yes, and we are confident of winning a majority in September."
However, a Better Together spokesman said: "This is yet another poll confirming that the majority of Scots want us to stay in the UK. The closer we get to the vote itself, the more people are thinking seriously
about the consequences of separation for our pound, pensions and public services. It's no surprise that the majority of Scots are saying no thanks to independence."
Tom Costley, head of TNS Scotland, said it had "consistently" found a significant number of undecided voters among those who said they were certain to vote. He said: "This month that proportion of the certain-to-votes has fallen from 22 per cent to 18 per cent - evidence that people are now beginning to form an opinion as the polling date nears."
Of those uncertain voters, 13 per cent said they were inclined to vote Yes and 12 per cent to vote No, with the remainder unsure.
Mr Costley said: "If we strip out all those who are committed to or at least sympathetic to one side or another, there are now relatively few people who say they are certain to vote but are completely undecided. We are finding only 13 per cent of certain-to-votes are expressing no inclination towards either side of the debate.
"Their decisions on h ow to vote could have a strong influence on the final result."