Judges are to consider whether a court can, in effect, sign a letter to the EU requesting a Brexit extension.
The Inner House of the Court of Session, Scotland’s highest court, is being asked to act directly if Boris Johnson refuses to request a delay.
The letter is a key provision of what is known as the Benn Act, by which MPs hope to prevent a no-deal Brexit.
The court will also hear an appeal against a ruling that Mr Johnson can be trusted to apply the law.
Lord Pentland said following an earlier hearing that there could be “no doubt” that the prime minister had agreed to abide by the law.
As a result, he said there was no need for “coercive orders” against the UK government or against the prime minister.
And he said it would be “destructive of one of the core principles of constitutional propriety and of the mutual trust that is the bedrock of the relationship between the court and the Crown” if Mr Johnson reneged on his assurances to the court.
The parallel case requesting that the court communicates directly with the European Union involves the exercise of the nobile officium power.
This is described by the Judiciary of Scotland website as a mechanism by which “the court may, within limits, mitigate the strictness of the law and provide a legal remedy where none exists”.
The case has been brought by businessman Dave Vince, Jolyon Maugham QC and Joanna Cherry QC, who is an SNP MP.
They argue that the court should step in to request a Brexit extension if the prime minister illegally refuses to do so.
In such circumstances, a letter could be signed by an official of the court.