Speaking at PMQs on Wednesday, Burnham said that the rules governing when a repeat of the 2014 vote can be held should be “exactly the same” as those for an Irish reunification referendum.

He made the comment when questioned on the Good Friday Agreement by SNP MP Chris Law. The agreement states that the UK Northern Ireland Secretary “shall” call a referendum on Irish reunification if it looks likely that the people would vote in support.

Writing on social media, John Swinney said: “To go from ‘off limits’ to this is an acceptance of the reality that the people of Scotland will decide their own future – not the UK Government.

“For the first time since 2014, a British Prime Minister accepts that majority support for a referendum should mean one takes place.”

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SNP MP Pete Wishart also welcomed Burnham’s comments, saying: “Very important response to Chris Law’s question @PMQs.

“For the first time the UK Gov has set out the conditions for an indyref. The Prime Minister says it would be the same as NI and would be dependent upon the securing of a majority in support.

“Real progress, at last.”

At Prime Minister’s Questions, SNP MP Law had said: “In response to my question last week, the Prime Minister stated that he is now very aware of every word in the Good Friday Agreement and will stick to it 100% as Prime Minister.

“So he will therefore know that the Northern Ireland Act contains a provision for a referendum on leaving the United Kingdom, but no equivalent provision exists within the law for Scotland.

“Does the Prime Minister recognise the people of Scotland have the same right, the equal right to choose their own future, and that the conditions for a second independence referendum should be set out in law?”

Burnham responded: “He mentions the Good Friday Agreement, and I will stick to it 100%.

“And I would also remind him on that question of a border poll, it is to be considered by the Northern Ireland Secretary when there is a clear consensus in the country, when public opinion has changed to the point where the call has to be considered.

“I would say exactly the same situation in Scotland.”

Burnham then added: “I am not aware that there is a majority of public support for another referendum, and until that changes, Mr Speaker, there won’t be one.”