Theresa May has time to give Scotland a special Brexit deal to avoid a second independence referendum, the SNP’s deputy leader has said.

Angus Robertson called on the Prime Minister to offer a compromise to “protect Scotland’s place in Europe” in exit negotiations.

His comments suggest a commitment from Mrs May to try to keep Scotland in the European Union (EU), or at least the single market, would be enough to avoid a second independence vote which Nicola Sturgeon announced on Monday she would seek parliamentary permission for.

An SNP source denied reports the First Minister would attempt to get an independent Scotland into the European Free Trade Association (EFTA), which includes Norway and Iceland and participates in the single market, rather than rejoin the EU as a full member.

The comments came as a new report found support for Scottish independence is higher than ever before but the “potentially divisive” issue of the European Union may make it difficult for nationalists to win a second referendum, and two separate polls put support for independence at 43% and 47% once the undecided were excluded.

Mr Robertson told the Guardian the Conservatives were “boxing themselves into a very dangerous corner”.He said: “There may only be days, may only be weeks, but Where all of our efforts are currently focused is trying to convince the UK Government to come to a compromise agreement protecting Scotland’s place in Europe.

“If that road runs out and if we have to have that referendum, we will be turning our attention to making sure that we are making the case publicly, intellectually and in every other way so people understand the choice of a hard Tory Brexit Britain or a Scotland able to maintain its relations with the rest of Europe.”

Scottish Conservatives leader Ruth Davidson said: “How can he say the SNP is focused on negotiations with the UK Government when Nicola Sturgeon has just broken off those talks to unilaterally declare another divisive referendum on independence?

“Everyone knows where the SNP has invested all its attention since the EU referendum - in trying to break up Britain.”

The latest ScotCen Scottish social attitudes survey suggested there is a “much higher” level of support for independence “than ever existed beforehand” - with this recorded at 46% in 2016, compared to 39% the previous year and 23% recorded in 2012, the year the previous referendum campaign began.

Meanwhile, a Survation poll for the Scottish Daily Mail found 46% of Scots do not want a second independence referendum to be held before the UK quits the EU while 41% were in favour, 9% backed neither option and 4% said they did not know.

Survation questioned 1,019 people in Scotland between March 8 and March 13, and found 36% want the Prime Minister to refuse to give Holyrood the power to stage another independence ballot while 31% said she should allow it.

The poll also found that 48% would vote No again if there was another referendum. Support for independence was 43% while 9% said they were undecided.

A YouGov poll for the Times suggested 57% of Scottish voters want to stay in the UK and 43% want independence, once “don’t knows” and those not prepared to vote were excluded.