Just 29 per cent said a vote should be held before the end of 2023, while 60 per cent said another vote should not be held in that timeframe.
Critics said the poll showed voters want the Scottish Government to “prioritise what really matters to them – not the SNP’s obsession with constitutional division”.
Nicola Sturgeon has repeatedly said she wants to hold a second independence referendum next year, although the UK government is unlikely to agree to this.
Survation polled 1,050 adults in Scotland for pro-UK campaign group Scotland in Union between April 29 and May 3.
It asked which was closest to their view, that "another referendum on Scotland leaving the UK should be held before the end of next year” or that it should not.
Using the question "should Scotland remain a part of the United Kingdom or leave the United Kingdom?”, 58 per cent of respondents said they would vote to remain and 42 per cent said they would vote to leave, once undecideds are removed.
Asked what the Scottish Government’s top three priorities should be, one-in-ten said an independence referendum – behind the NHS (61 per cent), economy and jobs (48 per cent), Covid-19 recovery (30 per cent), education (26 per cent) and housing (21 per cent).
Pamela Nash, chief executive of Scotland in Union, said: “Whatever SNP politicians claim about the council election results, it is clear the people of Scotland do not support their timetable for a divisive second referendum next year.
“Voters want the government to prioritise what really matters to them – not the SNP’s obsession with constitutional division.
“And once again, this poll has confirmed that a significant majority of people in Scotland want to remain part of the UK.
“Scotland’s best days are ahead of us as part of the UK, ensuring we can bring communities together and use the strength of our shared economy to invest more in the NHS, schools and local services.”
An SNP spokesman said: "The people of Scotland delivered a cast-iron democratic mandate for an independence referendum in last year’s Holyrood election when they returned the SNP with the biggest share of the vote of any party in the history of devolution and elected a record number of pro-independence MSPs.
"Just this week, support for the SNP was reinforced by our best ever local election result.
“Consistent polls have shown strong support for independence, and in many cases a majority.
"Attempts to block the democratic mandate delivered to the SNP are unsustainable and undemocratic.
"Scotland's future will not be dictated to by Boris Johnson and the scandal-ridden Tories whom Scotland have consistently rejected, but rather by the people who live and work here."
Speaking to journalists yesterday, Scottish Conservative leader Douglas Ross said Scots "do not want another independence referendum on Nicola Sturgeon's timescale".