The poll, undertaken by Redfield and Wilton Strategies for the political website, Politico, interviewed 1,000 Scottish voters.
It also indicated a continued lead for No if a second referendum was held, with 47 per cent of voters stating they would back No and 44 per cent stating they would back Yes.
Close to one in ten of Scots are undecided, the poll states.
Nicola Sturgeon could find herself at loggerheads with Scottish public opinion if she chooses to hold a referendum without the agreement of Westminster and Boris Johnson, the poll suggests.
The SNP has always stated that it wants to hold a legal referendum and has distanced itself from a so-called ‘wildcat’ referendum held without the consent of Westminster.
However, there is the possibility of a court challenge should the Scottish Parliament pass – as it is expected to – a referendum bill during this parliamentary year.
The only other route to a referendum is for Westminster to agree to hold one, as it did when it signed the Edinburgh Agreement prior to the 2014 vote.
The poll states that almost half – 43 per cent – of Scots said they agreed that a referendum should only be held in Scotland if the UK Government agreed to hold one, while 38 per cent disagreed.
When don’t knows were excluded, the poll indicated that just over half – 53 per cent of voters – agreed that the UK Government should be on board for a referendum to take place.
Voters are also split on the timeframe to hold another referendum with 41 per cent supporting a referendum in the next five years and 42 opposing one.
Stronger opposition is found for a referendum in the next year which is opposed by half of Scots and backed by just over a third (34 per cent).
Scots also agree with the UK Government’s Scotland Secretary, Alister Jack, who said that a vote should only happen if 60 per cent of Scots want one.
This was opposed by only 25 per cent of Scots, the poll states.
Alex Salmond remains the most unpopular politician in Scotland according to the poll with a net approval rating of -57, with former Labour leader Jeremy Corbyn also receiving a negative approval rating of -43.
Boris Johnson also remains far more unpopular overall than Nicola Sturgeon with a net approval rating of -38, while the First Minister’s popularity is at +14, lower than its heights during the worst of the pandemic and pre-election.
Keir Starmer is another struggler in the popularity stakes, with 19 per cent of Scots approving of his leadership, one percentage point less than Johnson.
He is, however, less disliked by Johnson, giving him a net approval rating of -19.
The Scottish Labour leader, Anas Sarwar, is by contrast liked by the public with a net approval rating of +5, while potential future prime minister, Rishi Sunak, also riding the crest of the furlough wave with a net approval rating of +3.