The High Court decided it was unlawful for the Government, to notify the European Union of Brexit, and so start the formal two year process of the UK's withdrawal from the EU without reference to Parliament.

Now it is the turn of the Supreme Court to consider the same constitutional question. Initially set down for a two day hearing, the Supreme Court has now scheduled four days. The fully televised hearing starts on Monday 5 December 2016.

As the underlying issue is the political future of the United Kingdom and its relationship with the European Union, the Supreme Court is sensitive to public perception.

Some reactions to the High Court's decision sparked off a controversial debate on the independence of the judiciary, and questioned whether its judges had decided against the Government because of their political views. The Prime Minister Theresa May contributed to this debate by endorsing both the independence of the judiciary, and the media's freedom to say that the judiciary is not independent.

Now the full panel of eleven Supreme Court judges will hear the Government's appeal. Eleven may be the largest panel to have heard a single appeal in the court's history.

The landmark nature of the constitutional question needs no emphasis. But the implications for the reputation of the judiciary has led the Supreme Court to take the unusual step of stating on the Brexit case's official webpage that its judgments are not based on judges' personal political views:

"The Justices are aware of the public interest in this case and the strong feelings associated with the wider political questions of the UK's departure from the EU (which we stress are not the subject of this appeal). The Justices' duty is to consider the legal questions impartially, and decide the case according to the law. The range of parties and interveners already before the Court is such that the Justices are satisfied that all issues and points of view will be represented."

Since the High Court hearing the number of parties involved in the Supreme Court appeal has increased. The Northern Irish, Welsh and Scottish governments are set to present arguments to the Court concerning the case's impacts on their devolved jurisdictions. Their arguments concern whether their legislatures should have a say in the triggering of Article 50 in relation to its consequences for Northern Irish, Scottish or Welsh voters. This has resulted in the longer period for the appeal to be heard.

The Prime Minister has been optimistic about the Government's chances at the Supreme Court hearing – "We have a good argument", she told the House of Commons on 16 November.

But other voices have also been reported suggesting otherwise; that the Supreme Court Justices could decide 11–0 against the Government. Such an outcome would be likely to involve a vote in the Westminster Parliament to allow the Government to trigger Article 50, but it might also extend to further approvals being required from Northern Ireland, Scotland or Wales.

The Supreme Court's website confirms that we should expect its judgment in the New Year.

If the decision goes against the Government, then its schedule for triggering Article 50 by March 2017 may well be in jeopardy; and delay is likely for as long it takes for the necessary Parliamentary votes to take place unless a Bill is rushed through. Another unknown is the extent of negotiations in the House of Commons and the House of Lords over the content of new legislation to regulate the process of exiting the EU.

Generally discounted is the outside chance that delay could arise due to a reference to the European Court of Justice in Luxembourg, for guidance on whether the triggering Article 50 is reversible.

For anyone interested in going to the Supreme Court to attend the appeal hearings, its website warns that seats will be hard to come by due to the public interest in the case:

Due to limited space in the main courtroom, you are strongly advised to watch online using one of the various live web streams … rather than travel to the Court and risk the disappointment of not getting a seat in court. The Supreme Court's live feed will cover the entire proceedings, with no delay."