And in a further blow to the SNP, less than a third of Scots back Nicola Sturgeon’s drive for a second independence vote.
The YouGov survey showed just 44 per cent back the break-up of Britain, lower than in September 2014.
It comes as the SNP closes its so-called national survey, which sought the views of Scots across the country on the constitution.
Support for the Scottish Conservatives has risen in both the constituency and regional opinion polls, YouGov revealed, while leader Ruth Davidson has double the approval rating of the First Minister.
Nicola Sturgeon previously said the only grounds for calling another referendum would be an expansion in public support for independence.
Scottish Conservative leader Ruth Davidson said:
“The SNP has spent the last 12 weeks promoting a so-called national survey to convince the people of Scotland of the need for a second referendum.
“Today, it got its answer – fewer than than one in three want another referendum, the lowest since the 2014 vote.
“My message to Nicola Sturgeon is clear – we voted on independence two years ago. Move on.
“Stop disrespecting the majority of the people of Scotland by continuing to push your divisive and unwanted second referendum, and get on with the job you were elected to do.”