Nicola Sturgeon is warning that there will be an “unstoppable clamour” for a second Scottish independence referendum if Scotland is taken out of the EU against its will.

In a speech in Brussels on Tuesday, the SNP leader spoke of a “groundswell of anger” and a “strong backlash” if Scotland were to be taken out of the EU by a UK-wide referendum.

During her first speech in Brussels since becoming first minister, Sturgeon insisted that “positive changes” can be made from within the existing treaty.

She emphasised the difference between the Scottish and UK governments’ stances on Europe, as the British prime minister, David Cameron, moves forward with his planned referendum on EU membership.

In an address at the European Policy Centre, the first minister highlighted the benefits that EU membership brings to Scotland, including the boost to the economy brought by the 171,000 people born elsewhere in the EU but living and working in Scotland.

Sturgeon said: “Polls in Scotland consistently show strong support for EU membership. That is why we will propose a ‘double lock’, meaning that exit from the European Union would only be possible if all UK nations agreed. That way Scotland couldn’t be forced out of the European Union against our will.”

The SNP leader added: “I previously stated my view that if Scotland were to be taken out of Europe despite voting as a nation to have remained, it would provoke a strong backlash amongst many ordinary voters.

“Quite what the result of that would be no one can perceive but I’ve stated before that this could be one scenario producing the kind of material change in circumstances that would precipitate popular demand for a second independence referendum.

“Bluntly, I believe that the groundswell of anger amongst many ordinary people in Scotland under these circumstances could produce a clamour for another independence referendum that may well be unstoppable. Of course it is open to the UK government to stop that happening, to guard against that scenario, by agreeing to the double majority provision.”

Her words came after Cameron’s tour of European capitals last week where he tried to drum up support for the reform of Britain’s relationship with the EU he hopes to secure before the referendum promised by the end of 2017.

With a legal challenge against Scottish plans for a minimum alcohol price making its way through the European courts, Sturgeon used her address, to call for member states to be given autonomy in key areas, such as public health policy, and for the development of a single EU market in energy and digital services.

The Scottish government also wants more localised discretion in implementing regulations to make EU policies “more proportionate and less burdensome”, pointing to changes made to the common fisheries policy last year.

Sturgeon delivered her speech almost 40 years to the day since the UK held a referendum on whether or not to stay in the European Economic Community in 1975.

She said that, in addition to the “double majority”, the Scottish government would seek to change the UK government’s referendum bill to extend the franchise to 16- and 17-year-olds and allow EU citizens from outside the UK to vote.

Sturgeon said: “It is incomprehensible to us, for the EU referendum, that the UK government is proposing to grant the right to vote to the citizens of three other EU countries – Ireland, Malta and Cyprus – but not the remaining 24.

“Denying them a say, on an issue which affects them so directly, is unfair, undemocratic and unjustifiable.”

The first minister restated her commitment to the European convention of human rights, saying that it “defied belief” for any government to move away from it, and called for the UK to do more to help refugees in the Mediterranean.

She said: “Alongside our openness to people from the EU, Scotland also recognises its obligations to refugees. We believe that all EU members have a role to play in helping those who have fled conflict and persecution and come to Italy or Greece from across the Mediterranean.

“That’s why the Scottish government has urged the UK to participate fully in proposed EU action – such as on relocation and resettlement – and it’s why we have made it clear that Scotland is willing to take our fair share of refugees.”

Speaking after the address, Sturgeon denied the prospect of another referendum was a threat that would be used as leverage any time there was a disagreement with UK government policy.

She said: “Simply stating fact and offering a solution to a perceived problem, I don’t accept that that’s a threat. I’m trying to be constructive here and we will continue to be so, both as the bill goes through the House of Commons but [also] in the wider debate.”