The case of The Queen on the application of Miller and Dos Santos v. the Secretary of State for Exiting the European Union is not about overturning the UK's referendum decision to leave the European Union. It actually addresses the question of whether Article 50 may be invoked without a specific authorisation by Parliament. In other words, and despite the best attempts of some of the nation's tabloid press to muddy the waters, the legal arguments are all about "how" and "who", and not about "whether" to start the process of leaving the EU.

What are the legal arguments?

The government's case, heard initially in the High Court, is that it is a matter for ministers to decide when and how to trigger Article 50, using the Crown prerogative (a bundle of government powers which are not conferred on ministers by statute, but which UK common law recognises as being able to have legal effect in certain circumstances). The other side's argument is that this would mean ministers would be taking action to remove important legal rights conferred by Parliament on UK citizens and businesses when the original European Communities Act 1972 (the 1972 Act) was passed. Their position is that the 1972 Act means that ministers could only have such powers if granted to them in statute, and no statute, either expressly or by necessary implication, grants such powers.

On 3 November, the High Court decided unanimously against the government, holding that ministers have no power to trigger Article 50 unless and until Parliament confers such power on them. In its judgment the High Court found the government's arguments "flawed" at a "basic level", because they gave "no value to the usual constitutional principle that, unless parliament legislates to the contrary, the Crown should not have power to vary the law of the land by the exercise of its prerogative powers".

The Supreme Court

The government appealed to the Supreme Court, and that hearing took place between 5 and 8 December. While the arguments presented were broadly the same as those advanced in the High Court, the appeal is a defining moment in the court's history. "The Brexit Appeal", as it has come to be known, was heard by all 11 of the Supreme Court's permanent Justices, including those from Scotland and Northern Ireland. This is the first time all of the permanent Justices have presided over a case since the Supreme Court replaced the Appellate Committee of the House of Lords as the highest court in the United Kingdom, on 1 October 2009.

The Supreme Court was established for many reasons, but not least: to achieve a complete separation between the UK's senior judges and Parliament; to emphasise the independence of the Justices; and to increase transparency between Parliament and the courts. Never have these distinctions been – and been seen to be – more important than now. The court system is a fundamental pillar of the constitution, being the final arbiter between the citizen and the state – none more so than the Supreme Court, as the highest appellate court for civil cases in the United Kingdom.

A dis-United Kingdom?

In recognition of the political and constitutional issues involved (the majority of voters in Scotland and Northern Ireland actually voted to remain in the European Union in the referendum), a number of parties, including the chief law officers for the devolved Scottish and Welsh governments, QCs representing Northern Ireland and indeed the Independent Workers Union of Great Britain, were allowed to make submissions in the Supreme Court appeal. The role, status and involvement of the different national parliaments in the process is another first for the Brexit Appeal. Richard Gordon QC, representing Welsh ministers, informed the Supreme Court that Brexit has "split the UK in to four parts" and "is one of the most divisive political events in decades".

What next?

If the Justices allow the appeal and reverse the High Court decision, this will enable ministers to trigger Article 50 without a Parliamentary vote. Should they uphold the High Court decision, however, it is thought that they will include a clear statement of exactly what Parliament will need to do. An Act of Parliament might be required, or it may be that a resolution is deemed sufficient. In the case of an Act, ministers would then have to prepare a Bill to give them the necessary authority, and, once a Bill is in play, members of both Houses of Parliament are likely to want to introduce amendments to it that go beyond simple authorisation to give an Article 50 notice. As a result, the government may be forced not only to amend its current timetable (of triggering Article 50 by the end of March 2017), but also to concede to Parliament a greater role in the exit process than it has been willing to do so far. Whatever the outcome, the Brexit Appeal is the biggest challenge that the Supreme Court has faced since its creation. Its decision, expected in January 2017, is eagerly awaited by legal, constitutional and political experts across the entire common law world.