//...it's still the case that without agreement come the deadline, we have left.//
Unfortunately you have left out the small matter of the PM being compelled by Parliament to ask Brussels for an extension to 31st January, OG. Worse than that, if the EU says "No, not 31st January but 31st Decemeber 2050, he has to come back and put that proposal to Parliament. Being composed mainly of Remainers, it is likely that Parliament will accept that generous offer. Such is the law which MPs passed last week.
Back to the question, the English High Court took a different view to the Scottish equivalent. They did not look at the reasons for the prorogation. They simply declared that it was not a judicial matter. They said that the court was not to be used to "...exert hitherto unidentified power over the Executive branch of the State in its dealings with Parliament". Hopefully similar common sense will reign in the Supreme Court next week. If it doesn't we can be prepared for each and every decision made by the government under its executive powers to end up over the road in the Supreme Court for approval. Do we really want that? The matter goes far beyond Brexit.