The court will rule if the UK can withdraw the Article 50 trigger notice unilaterally, as argued by many experts including the author of the mechanism.
A cross-party group of politicians secured the go ahead for the case from a Scottish court in September, which referred it to the Court of Justice of the EU (CJEU).
With Theresa May’s Brexit deal seemingly doomed to defeat in a Commons vote next month, the controversy over whether Article 50 can be revoked is likely to become crucial.
Now the Supreme Court has rejected the appeal by the government against the Scottish ruling because it did not “constitute a final judgment”.
In a statement, it said: “As both this court and the CJEU have made clear, the preliminary ruling is merely a step in the proceedings pending before the national court.
“It is that court which must assume responsibility for the subsequent judicial decision.” The hearing is on 27 November.
Lord Kerr, a former diplomat and the author of the Article 50 notice, has argued the British government can withdraw its letter and stop the process if it wished to.
He was backed by Jean-Claude Piris, former head of the European Council’s legal service, who said earlier this year: “Article 50 is based on the principle that withdrawing from the EU is a unilateral decision. Nobody can force a state to leave.
The prime minister has also been accused of suppressing a formal legal opinion that parliament has the power to reverse the exit notice.
Lawyers for the Department for Exiting the European Union (DExEU) had launched today’s appeal in the Supreme Court.
The initial case had been brought by Labour MEPs Catherine Stihler and David Martin, Joanna Cherry MP and Alyn Smith MSP of the SNP, and Green MSPs Andy Wightman and Ross Greer, together with lawyers from the Good Law Project.
The Scottish decision had overturned an earlier ruling when it was said the question being asked was “hypothetical” and the conditions for a reference had not been met.
In September Lord Carloway said it was clear that MPs at Westminster would be required to vote on any Brexit deal agreed by the EU and the UK government.
The CJEU would not be advising parliament on “what it must or ought to do”, but “merely declaring the law as part of its central function”.
Lord Carloway added: “How parliament chooses to react to that declarator is entirely a matter for that institution.”