Support for Scottish independence has risen since British Prime Minister Theresa May came out last month in favour of Britain making a clean break with the European Union when it leaves the bloc, an opinion poll shows.

The poll still showed a slim majority opposed to independence, but the ruling Scottish Nationalist Party said the fact that almost half those asked said they supported secession indicated that sentiment was shifting and could embolden calls for a new vote.

In 2014, Scots voted roughly 55 per cent to 45 per cent to remain in the United Kingdom. But last year's Britain-wide vote to leave the EU changed the landscape because a majority of Scots backed staying in the EU.

The pro-EU SNP, the biggest party in Scotland's parliament, has said that there should be another independence vote if its views on Brexit are rejected. May has repeatedly said she sees no need for one.

A majority of those asked in the BMG survey, 51 per cent, still opposed independence, the survey showed, but that number fell by three and a half points while the number supporting secession rose by the same amount, to 49 per cent.

The proportions were calculated after "don't know" votes were removed in the survey of 1067 Scottish residents, which was conducted for the Herald Scotland newspaper.

A demand for a second independence referendum from Scotland's devolved government would throw the United Kingdom into a constitutional crisis just as PM May seeks to negotiate the terms of the Brexit divorce with the EU's 27 other members.

Scotland has a population of around 5.3 million, according to the last census, slightly more than 8 per cent of the United Kingdom's population as a whole. It was an independent kingdom until joining England in the Act of Union in 1707.

A report in Dundee-based newspaper the Courier on Wednesday said May believes Scottish First Minister Nicola Sturgeon could next month demand a second referendum on independence and is privately working on a strategy to deal with this.

Asked for comment, a Scottish government source said the government was still in a negotiation process with the United Kingdom which continues in good faith but it was "interesting to see that the UK government appears to accept the Scottish mandate to decide its own future, should that become necessary".

However, in his response to the report, a spokesman for May said the UK government did not believe there should be a second referendum.