The application must be submitted by 21 September and the Lord’s Counsel and the Solicitor General of Scotland – representing the interests of the UK Government in the case – will have two weeks to respond.
Oral arguments in the case are scheduled to be heard on October 11 and 12. The date of the final decision has not yet been announced.
The Lord’s attorney referred the prospective independence referendum bill to court in July, with her argument relied heavily on the fact that any referendum would not be self-executing, but merely “advisory”.
This means that if the majority of Scots say they want to leave the union, Scotland will not become independent immediately, but the referendum could serve as the basis for independence negotiations.
“This crisis in the UK is much worse than in other developed countries because of Brexit, which Scotland voted against but was powerless to stop.”
Scottish voters rejected independence in 2014, but the Scottish National Party says Brexit, which a majority of Scots opposed, means the question must be asked for a second vote.
Pro-independence parties won a majority in last year’s Scottish parliamentary elections. Ms Sturgeon says this gives Holyrood the mandate to hold a new independence vote.
The UK government has refused to agree to a new referendum, saying the matter was settled in 2014 and there are bigger priorities people in Scotland want to focus on.
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Meanwhile, SNP Westminster leader Ian Blackford has said a general election should be held sooner rather than later after Liz Truss enters Downing Street.
Mr Blackford said a general election should be held because Ms Truss appeared to be making proposals that were not in the 2019 Conservative Party election manifesto.
He added that it would give people north of the border the opportunity to have their say on whether Scotland should be an independent country.
Asked if he would like a general election sooner or later, Blackford told the BBC: “It is very, very simple, for the very simple reason that what Liz Truss is now proposing was not in the Tory manifesto for the 2019 election.
“First of all, let’s provide the support that families, those businesses need. Let’s get that done, and the right thing to do next is get this up to the people, have that general election and let the people in Scotland have their say, and I think critically their opinion about Whether or not Scotland should be an independent country.
Ms Truss opposes the Scottish government’s plans to hold a second independence referendum next year.
Asked if he would treat early elections as an actual referendum, Blackford said that if a referendum was not possible, the actual decision in a general election was the “hypothetical situation”.
Sturgeon said that if the Supreme Court ruled against the Scottish government, it would treat the next general election as a “de facto referendum”.
Mr Blackford told the BBC: “First of all we have a Supreme Court hearing in October, I can’t see we’re going to have an election before that anyway so let’s wait and see what happens.
“If we win this case in the Supreme Court, that means we have a referendum in October 2023 and that’s what we should focus on.
“Of course if, for whatever reason, we can’t make it happen, then that factual decision being made by the people in a general election becomes the default position.”