Burnham was responding to a question at Prime Minister’s Questions from Dundee SNP MP Chris Law.
Law noted that Burnham had said he would stick 100% to the terms of the Good Friday Agreement in Northern Ireland and noted that the agreement includes a provision on what would trigger a referendum on leaving the UK.
He then asked whether the conditions for initiating a similar referendum in Scotland should also be set out in law.
Burnham replied that the Good Friday Agreement said a border poll “be considered by the Northern Ireland Secretary when there is clear consensus in the country—when public opinion has changed to the point at which the call has to be considered”.
He continued: “I would say that it is exactly the same situation in Scotland. I am not aware that there is majority public support for another referendum, and until that changes, there will not be one.”
A referendum on Scottish independence in September 2014 saw the country vote to remain part of the UK by a margin of 55% to 45%.
Burnham first made his “off limits” comment when he met Swinney for the first time after becoming prime minister, when he travelled to the Commonwealth Games in Glasgow in July.
