Just a few days ago ICM put support for Remain and Leave across Britain as a whole at 50 per cent each (once Don’t Knows are excluded). In contrast, our Scotland poll today puts Remain on 59 per cent, Leave on 41 per cent.
However, this is the first time that any poll has suggested that Remain might win less than 60 per cent of the Scottish vote.
Moreover, today’s result comes on top of another poll on Friday that suggested there has been a five-point swing towards Leave during the past four weeks.
The Remain camp may not be able to count on an overwhelming Scottish vote in its favour after all.
Not least of the reasons is that the SNP’s advocacy of EU membership is not proving to be as persuasive as the party might like. According to today’s poll, those who voted for the SNP in last year’s general election are no more likely than Scots in general to say they will vote for Remain.
Indeed, all of the parties are having difficulty in persuading voters that they should follow their recommendation to back Remain. A majority of Conservative voters are inclined to vote to Leave, while even Labour faces the prospect that three in ten of its supporters will do the same.
The EU referendum is set to leave all of Scotland’s major parties with significant wounds to heal.
Meanwhile, of course, should the UK vote to Leave the EU, the question of whether Scotland should hold another referendum on independence is likely to arise.
Today’s poll confirms the message of previous polls that a UK vote to Leave could mean Nicola Sturgeon would have a difficult decision on whether to hold a second ballot or not.
On the one hand, it looks as though in those circumstances a majority would support independence. Once Don’t Knows are left to one side, 53 per cent say they would vote for independence in those circumstances, while only 47 per cent would vote to stay in the Union.
But that would be a slender reed on which to launch a second independence referendum. It is, after all, a ballot the SNP could not afford to lose. To do so truly would settle the issue for a generation.
Moreover, it is far from clear how easy the path towards keeping an independent Scotland inside the EU would be in the event that the UK had voted to leave. Just as in the case of the referendum 18 months ago, there may not be a straightforward answer to that question.
However, two-thirds (67 per cent) say that a second independence referendum should not be held until the issue has been resolved.
Perhaps it is not surprising after all that Nicola Sturgeon is so adamant that she does not want the UK to vote to leave.
• John Curtice is Professor of Politics, Strathclyde University