The Panelbase poll found just 48 per cent of people – excluding the don’t knows – would support independence if a referendum were held tomorrow. In April, support for breaking up the Union stood at 52 per cent.
Meanwhile support for remaining part of the UK in the poll, which was commissioned by The Sunday Times, is also up to four percentage points to 52 per cent.
Professor Sir John Curtice of Strathclyde University, said the results indicated "a cooling of the independence ardour" since the Holyrood elections last month.
The poll of 1,287 adults aged 16 and over found just 19 per cent of respondents believe an independence referendum should be held within the next 12 months – down 3 per cent from the polling company’s April survey – with 35 per cent supporting a vote in the next two to five years, up two percentage points.
However, 46 per cent of voters said there should not be another referendum in the next few years.
The poll also indicated 22 per cent of people believe independence will happen within five years, which is also a decline of 8 per cent since April, although almost a quarter believe it will happen between five and ten years.
Prof Curtice said the poll suggested "lowered expectations" on the independence question, which could now reduce the pressure on Nicola Sturgeon “to press the referendum button any time soon”, though he said the SNP could not afford the independence debate "to be off the boil for long".
He said: "Rather, the party needs to embark on a campaign to persuade more Scots of the merits of independence. Otherwise, Ms Sturgeon might find herself stuck with a promise to hold a referendum that she has little hope of winning."
The poll also suggests that in a Westminster election the SNP would win 52 seats, four more than at present, taking two from the Conservatives and two from the Scottish Liberal Democrats. Labour would retain its single seat.
A month on from the Holyrood election, the figures also indicated a drop in SNP support in both constituency and list seats. The party standing is down 2 per cent, at 46 per cent, in the constituency poll, and down 2 per cent to 38 per cent for the list.
Responding to the poll, Pamela Nash, chief executive of Scotland in Union, said: “The UK’s broad shoulders have helped every part of the country through this crisis, from protecting jobs to a successful vaccination programme, so it is not surprising that more people are recognising the benefits of remaining part of the UK.
“The Scottish Government should listen to what voters are saying and focus on the Covid recovery, which will take many years – and not re-open old divisions.
“As part of the UK we can build a recovery that leaves no community behind.”
A Scottish Conservative spokesperson said: "This poll confirms last month's election result that only the Scottish Conservatives can build Scotland's real alternative to the SNP."
The poll comes as the new chair of the Electoral Commission, John Pullinger, said the body could agree to a future demand by the SNP to hold a non-binding referendum on Scottish independence, even if the move is opposed by Boris Johnson.
Mr Pullinger said the commission was not just "a body of the UK Parliament", and would have an "independent discussion" with Scottish officials if they wanted "something to be done that helps them with their democracy".
His remarks put the commission on a collision course with the Prime Minister, who says he will reject a request for an "irresponsible and reckless" second referendum.
Nicola Sturgeon has said that May's Holyrood elections gave the SNP a mandate for a second poll, and there have been suggestions the Scottish Government may seek a unilateral poll if Westminster rejects a demand for a section 30 order.
Asked whether such a poll could take place if Mr Johnson refused the request, Mr Pullinger said: "That is what I've read."
He added: "The UK Electoral Commission is also the electoral commission specifically for Scotland and Wales. We have a direct reporting line to Scotland and Wales. And, as of April this year, we are directly funded by Scotland and Wales too.
"If the Parliament in Scotland is wanting something to be done that helps them with their democracy, we will have an independent discussion with them about whether it's appropriate for the commission to support that."
Meanwhile constitutional experts have warned that if the UK Government attempts to change the franchise in a second referendum, it could invalidate the result.
Reports have suggested Boris Johnson may allow Scots living anywhere in the UK to vote on independence, but experts have said there could be practical problems identifying who is eligible, and could lead to a challenge of the result.
James Mitchell, professor of public policy at Edinburgh University, said he doubted the suggestion to extend the electorate was serious.
“There would be practical problems identifying who would be eligible,” he said.
"Would this extended electorate have to apply to vote? Presumably there would need to be a campaign to inform potential electors elsewhere in the UK.
“If it included Northern Ireland, we can be sure that many would vote according to preferences related to Northern Ireland’s constitutional status and with scant regard for the Scottish question.”
Prof Mitchell said any future referendum would require agreement in advance of any campaign on the rules, conduct and how the results should be interpreted.
“There would be little point holding a referendum if the result was disputed or challenged fundamentally,” he said.
“The problem is that any unilateral change to rules by either government would likely lead to boycott, undermining turnout and thereby de-legitimising the result.”
Dr Alan Renwick, deputy director of the constitution unit at University College London, said the UK Government had “essentially accepted” the principle that Scotland had the right of self-determination in the Edinburgh Agreement, which set out the terms for the 2014 referendum.
He said: “Given that it has accepted that, then it ought to accept the principle that it has a duty in the context of any referendum to enable the people of Scotland to exercise that right fairly.
“If you try to tailor the franchise to a particular vote you just end up politicising the franchise and it becomes not a matter of principle, but a matter of political power. That delegitimises the vote.
“So if the Union won very narrowly and it was clear it had won only because the franchise had been changed from the normal franchise, then that doesn’t produce a result which is going to command universal respect by any means.”