Despite the First Minister hoping to keep free movement and stay in the single market, the research by NatCen found 62% thought trade and immigration rules should match those elsewhere in the UK.
Some 64% said EU migrants should face the same restrictions as those from outside the bloc – a far cry from SNP policy.
Nicola Sturgeon at the recent SNP conference in Aberdeen
Professor John Curtice, a highly respected political academic and senior research fellow at NatCen, said the research called into question Ms Sturgeon’s justification for a fresh independence vote.
“This means that on immigration in particular voters in Scotland seem to be more in tune with the stance taken by the UK government than that adopted by the Scottish Government,” he said.
“Indeed, it seems that even amongst those who voted Yes to independence in September 2014 there is a limited appetite for having a more liberal regime on EU migration in Scotland than there is in England and Wales.”
He said it was “far from clear” that SNP fears about Brexit will stoke fresh support for independence if Theresa May secures a free trade deal and freedom of movement curbs in her talks with Brussels.
It comes as Brexit Secretary David Davis formally told Ms Sturgeon her plan to keep Scotland in the single market while the rest of the UK leaves would be undeliverable.
Ms Sturgeon has vowed to press ahead with a new independence referendum, despite Theresa May saying the time was not right, after Holyrood voted to request the necessary sign-off from Westminster.
Writing in the Guardian today, she said: “We must now ensure that people in Scotland are given a choice between the hard Brexit deal now being negotiated, and independence.”