Voters also believe independence would be better than a negotiated Brexit settlement. However, when asked how they would vote in an independence referendum, voters would still back the Union by 53% to 47%.
A Panelbase survey of 1,028 voters found 59% of respondents agreed that independence would be better than a no-deal Brexit, with 41% disagreeing.
When asked if independence would benefit the country more than staying in the UK after a negotiated Brexit deal, 53% agreed and 47% disagreed.
Just over half of Scots (51%) would back a fresh general election if Theresa May fails to get her Brexit deal through parliament, and 54% believe she should resign if defeated.
In a general election, the SNP would made modest gains at Westminster, with the poll putting their support at 37%, Labour and the Conservatives tied on 26%, the Liberal Democrats on 6% and UKIP and the Greens on 2%.
Analysis by Sir John Curtice, professor of politics at the University of Strathclyde, suggests that would translate into a gain of four MPs for the SNP, putting them on 39, while Labour would lose three seats, taking them down to four - making a minority administration supported up by the nationalists unlikely.
The Tories would retain 12 MPs, down one, and the Lib Dems would be unchanged.
“Although this poll suggests that support for independence may have edged up a bit, as things stand the nationalist movement still finds itself tantalisingly short of the support it needs to win a second independence referendum,” Mr Curtice told the Sunday Times, which commissioned the poll. “However, over half of those who voted no in 2014 still want Britain to remain part of the EU. Some of them at least find the choice between a UK that is leaving the EU and Scottish independence a tough one — and especially so, should the UK leave without a deal.
“In those circumstances over one in three 2014 No voters find it impossible to say which is preferable, while, even if there is a deal, one in five still finds themselves in that predicament.”
At Holyrood, the poll found that Nicola Sturgeon risks losing her pro-independence majority in the next Scottish election, due in 2021.
In the regional vote, the SNP is up three points on 38%, the Tories are unchanged on 26%, Labour are on 22% (up 2%), Lib Dems on 7% (down 1%), Greens at 6 % (down 1%) and Ukip on 1% (down 1%).
Those figures would leave the SNP on 57 MSPs, down six compared with the 2016 election, while the Tories would gain three, taking them to 34. Labour would gain three MSPs, taking them to 27, the Lib Dems would have seven MSPs, gaining two, and the Greens would lose two MSPs, leaving them with four.