The poll, undertaken by Survation for the independent election analyst Ballot Box Scotland, interviewed 1,002 Scots aged 16 and over between 24 and 28 March.
It suggests the SNP are on track for securing 44 per cent of all first preference votes in the council elections on May 5, with Labour well behind in second on 23 per cent and the Scottish Conservatives in third on 18 per cent.
In 2017, the SNP won 32 per cent of the vote, with Labour 20 per cent and the Conservatives on 25 per cent.
Only one party has registered above 33 per cent of the total vote share at council elections since the dawn of devolution with Donald Dewar’s Scottish Labour party doing so in 1999 with 36.6 per cent of the vote.
The SNP’s results in 2012 and 2017 were both 32.3 per cent, meaning a 44 per cent vote share would be close to matching record highs of Labour support prior to local government reorganisation in 1995.
In 1995, Tony Blair secured a result of 43.6 per cent which saw 613 councillors elected, though this was before the current Single Transferable Vote system was in place.
The poll indicates first preference support for the Liberal Democrats at six per cent, with the Greens on three per cent, Alex Salmond’s Alba party on one per cent, and independents who won 10 per cent of first preferences in 2017, on just one per cent.
Such a result for the SNP was described as “astonishing” by Allan Faulds, founder of Ballot Box Scotland, who warned the poll likely underestimates support for independent candidates and the Scottish Greens, whilst overstating SNP support.
He said: “If these findings are accurate, the SNP are on track to deliver an astonishing record result in May, and Labour would again become the second largest party at local government level, giving both parties reason to be cheerful.
"On the other hand, the Conservatives, Lib Dems, Greens and Independents would seem to be headed for worse results, and Alba’s support is pretty pitiable. That said, some of these figures are rather eyebrow raising when compared to other electoral evidence.
“It has proven particularly difficult to gauge support for Independents, who’ve collectively received at least 10 per cent of the vote at each of the last three elections, but only 1 per cent in this poll. Similarly, across the most recent batch of 18 local by-elections they contested, the Greens won 7 per cent of the vote and could thus be underestimated.
"Meanwhile polling ahead of 2017 was just as rosy for the SNP but support failed to materialise on the day. Collectively, this suggests there may be a particular challenge in capturing local voting intention via national poll – we’ll find out definitively either way in May."
Combining the total top three preferences, whereby a voter has indicated a preference for at least three parties, the SNP sit on 56 per cent, Labour 52 per cent, Green 37 per cent, Liberal Democrat 31 per cent, Conservative 27 per cent, independents seven per cent, and Alba seven per cent.
Mr Faulds added: “Findings on later preference use nonetheless make for fascinating reading.
"Whilst the SNP and Conservatives have solid first preference support, they were picked relatively rarely for later preferences, whereas the other three Holyrood parties were popular transfer options.
"This perhaps suggests the parties most rigidly defined by the constitution are putting off voters in the middle.”