Nicola Sturgeon has been accused of being out of touch with Scotland about Brexit after a major survey found almost two-thirds of Scots oppose her demand for a different deal and support Theresa May’s UK-wide blueprint.

The First Minister’s justification for a second independence referendum was severely undermined by the NatCen research, which found 62 per cent of Scots think trade and immigration rules should be the same as in the rest of the UK.

An overwhelming majority also support Mrs May’s plan to curtail free movement from the EU and oppose the First Minister’s insistence that it continue, with 64 per cent believing that immigrants from the Continent should be subject to the same restrictions as those from elsewhere in the world.

The research concluded that Scots’ views are similar to those of people in the rest of Britain and warned Ms Sturgeon that her argument that the Prime Minister’s Brexit blueprint justifies an independence vote “is unlikely to prove particularly persuasive.”

The Conservatives said the survey showed it was Ms Sturgeon who is out of touch with Scots’ views on Brexit, with even a majority of independence supporters demanding curbs on immigration.

It was published as David Davis, the Brexit Secretary, formally rejected Ms Sturgeon’s highly complex proposal for Scotland to stay in the EU single market when the rest of the UK comes out. This would have seen Scotland adopt completely separate trade and immigration regimes.