Nicola Sturgeon has warned Boris Johnson against blocking a fresh referendum on Scottish independence after a poll found a majority would now vote yes.

The first minister said it would be “undemocratic and unsustainable” for the Conservatives to oppose one after the poll by Lord Ashcroft put the yes vote at 52%, once don’t knows and non-voters were excluded.

The poll, the first since Johnson’s visit to Scotland last week, also found that most Scots want a fresh independence referendum by 2021, once undecideds were excluded. Previous polls had shown only a minority of Scots wanted a second referendum that soon.

In a further blow to pro-UK parties, it also found that a majority (52%) believed the yes campaign was likely to win, including a third of voters who rejected independence in the first referendum in 2014. Only 30% believed Scotland would now vote to remain within the UK after Brexit, and 18% did not know.

Speaking on Monday evening at an Edinburgh festival fringe event, Sturgeon said Ashcroft’s poll had picked up an increasing sense of urgency about the need for independence she had been seeing for some time.

Interviewed by the broadcaster Iain Dale, Sturgeon said: “I think there is growing support for independence in Scotland. And I think there is, accompanying that, a growing sense of urgency that if we don’t want to get dragged down a path – and I’m not just talking about Brexit here although largely that’s what I mean, but dragged down a sort of political path that we don’t want to go down – then we need to consider becoming independent sooner rather than later.”

Legally, the Scottish government can only stage an official referendum if the UK government gives it the powers under section 30 of the Scotland Act. Johnson has said he would refuse to do so.

Sturgeon tweeted: “Majority of people in Scotland now want #Indyref2 and would vote for independence, according to new poll in @HolyroodDaily – attempts by the Tories to block Scotland’s right to choose our own future are undemocratic and unsustainable.”

Majority of people in Scotland now want #Indyref2 and would vote for independence, according to new poll in @HolyroodDaily - attempts by the Tories to block Scotland’s right to choose our own future are undemocratic and unsustainable. https://t.co/Pft4esilCM — Nicola Sturgeon (@NicolaSturgeon) August 5, 2019

This is the first poll since March 2017 to show a narrow majority for independence. Until now, the pro-UK vote has enjoyed a small but consistent lead.

Johnson’s critics and opponents, including senior figures inside the Conservative party and the party leader in Scotland, Ruth Davidson, have long forecast that his election and his pursuit of a hard Brexit would boost support for independence.

Ashcroft, a former Tory party treasurer, found that 62% of Scots believed Brexit – regardless of whether that was with or without a deal – made independence more likely. That included 38% of Tory voters.

Despite repeated warnings from unionists that leaving the UK would be more economically and financially damaging to Scotland than Brexit, a narrow majority of voters (45%) said staying in the EU was more important than staying in the UK (43%, with 12% don’t knows).

Ashcroft’s data substantiates previous polls predicting that a Johnson premiership would help Sturgeon. However, since Ashcroft does not carry out regular polls on these questions and will not reveal which polling company carries them out for him, it is harder to compare this data accurately with previous polls.

Before his visit to Faslane submarine base and his meeting with Sturgeon last week, Johnson had insisted he would be a staunch defender of the union. He said it was “vital we renew the ties that bind our United Kingdom. I’m proud to be in Scotland today to make clear that I am a passionate believer in our great union.”