The ICM survey suggested a post-Brexit referendum would secure a Yes majority of 53 per cent and came as Nicola Sturgeon announced a new drive for independence.
The poll also suggested more than half (52 per cent) favoured holding a second referendum in the event of Scotland voting to remain in the EU but being forced out by votes cast across the rest of the UK.
Sturgeon has repeatedly said Brexit could trigger another attempt to break up the UK and at the SNP conference in Glasgow yesterday, the First Minister announced the party would start rebuilding the case for her “beautiful dream” .
“I can tell you that this summer the SNP will embark on a new initiative to build support for independence,” Sturgeon told activists.
The First Minister said the party would not attempt to “browbeat” people into joining the independence cause and would respect the views of those who support the Union.
But she added: “I know that many wanted to be persuaded in 2014, but ultimately didn’t find our arguments compelling enough. So we will listen to what you have to say.
“We will hear your concerns and address your questions – and in the process we will be prepared to challenge some of our own answers. Patiently and respectfully, we will seek to convince you that independence really does offer the best future for Scotland.”
ICM asked the 1,000-strong sample whether there should be a second independence referendum in the event of Scotland voting to remain in the EU, but being forced out by a vote to leave across the UK as a whole.
It found that 48 per cent believed there should be another referendum, against 44 per cent who thought there should not and nine per cent who didn’t know.
When the Don’t Knows were excluded, 52 per cent thought there should be a second independence poll and 48 per cent didn’t.
When asked how they would vote in a second referendum, 49 per cent said they would vote for independence, while 43 per cent said they would vote against it. Eight per cent said they didn’t know.
When the Undecideds were excluded, the poll found that more than half (53 per cent) would vote for independence – enough on paper to secure the break up of the UK.
But whether a lead of 53 per cent is enough for Sturgeon to call a second referendum is another matter entirely.
In the past she has said she will only call another vote when she is certain of winning. SNP sources have suggested she will not risk it until support for Yes is polling consistently above 60 per cent.
On the question of how Scotland would vote in the EU referendum, there was still a majority in favour of the EU with 50 per cent wanting to stay in; 35 per cent wanting to leave and 15 per cent who didn’t know. When the Don’t Knows were excluded, those wanting to stay out-polled those wanting to leave 59 per cent to 41 per cent.
The survey confirmed that Scotland appears more pro- EU than the UK as a whole, where polling suggests that the two campaigns are running almost neck-and-neck.
But as the first poll to put support for staying in the EU at less than 60 per cent, it also suggests that the Leave campaign is making gains in Scotland.
A spokesperson for the Europe Minister Humza Yousaf said: “This poll confirms the strong public backing for keeping Scotland in Europe. We have made clear that a UK-wide vote to leave the EU while Scotland had voted to remain would almost certainly spark strong public demands for another independence referendum – but we will continue to make the case for an “in” vote.”
A spokesman for the Scottish Conservatives said: “The people of Scotland voted decisively to stay part of the UK in 2014. The Scottish Conservatives will fight for those two million people whatever the outcome of the EU referendum.”
A Labour spokesman said: “We were told by Nicola Sturgeon that the 2014 referendum would settle the independence question for a generation. The key issue in Scottish politics now is about what we should do with the major new tax and spending powers heading to the Scottish Parliament.”