The Brexit judicial review case is scheduled to start in the High Court on Thursday, 13 October 2016.

The issue at the heart of the case remains what is the lawful way for the Government to trigger the UK's departure from the EU?

The lead claimants include Gina Miller, who has described the proceedings as "the biggest constitutional case for hundreds of years". The claimants' arguments have become clearer since last month with the court's release of their grounds of claim and the Government's grounds of resistance.

The claimants are seeking a declaration by the court that only with Parliament's approval can the Prime Minister, or the Secretary of State for Exiting the European Union, lawfully notify the EU of Brexit under Article 50 (of the Treaty of Lisbon 2007), and so trigger the two-year process to leave the EU.

The claimants believe that such a declaration is necessary following the Government's pronouncements that it alone can notify under Article 50.

The claimants' principal argument is that if the Government lodges an Article 50 notification without Parliament's approval, this would frustrate or take away British citizens' rights under the European Communities Act 1972, the domestic law through which the UK is an EU member.

The claimant's argument continues that only Parliament has the power to undo the 1972 Act. As Lord Pannick QC, representing Gina Miller, has put it, "an Article 50 notification could only lawfully be given if expressly authorised by an Act of Parliament."

A key legal principle underlying the claimants' argument is that no individual in government has the power alone to do acts that undermine citizens' rights granted by Parliament, such as EU rights flowing to the British people from the 1972 Act.

The Government's grounds of resistance, prepared by its QCs James Eadie and Jason Coppel, argue that the Government is free to issue an Article 50 notification whenever it chooses. The Government argues that doing so would be an administrative act of an international or diplomatic kind, traditionally reserved for the Government to make unilaterally through the "royal prerogative", an ancient authority inherited from the Crown.

The Government contends that it would be unconstitutional for the court to direct otherwise. The Government's reasoning here is that if the court gives the claimants the declaration they are seeking, the court "would be trespassing on proceedings in Parliament". This would mean the court using its power to instruct Parliament, whereas under the UK's unwritten constitution the powers of the court and Parliament should be kept separate.

On 13 September 2016, the House of Lords' Select Committee on the Constitution published its advisory Report "The invoking of Article 50". In this Report, the Committee advises on what role Parliament should play in taking forward the EU Referendum result.

The Committee – after consulting a former Supreme Court Justice among others – concludes that:

"It would be constitutionally inappropriate, not to mention setting a disturbing precedent, for the Executive to act on an advisory referendum without explicit parliamentary approval – particularly one with such significant long-term consequences. The Government should not trigger Article 50 without consulting Parliament."

The "disturbing precedent" the Committee refers to is the idea that if Parliament does not vote to approve the EU Referendum result, a new form of "direct democracy" will have emerged in the UK whereby Parliamentary sovereignty – a core principle of the UK constitution, exercised by MPs as the elected representatives of the people – is bypassed on a matter of great national importance. In the words of one (unnamed) Committee adviser, this would be "a very big shift away from our traditional constitution.” If the EU Referendum result is itself enough to trigger Article 50, a precedent could be set for a new source of supreme power in the UK: referendums, not Parliament.

The Prime Minister, Theresa May, has rejected such lines of argument, announcing that the Government will trigger Article 50 by March 2017 without the need for Parliamentary approval. "The people have spoken, we will deliver on that", she said on 2 October 2016. This message was repeated by David Davis as Secretary of State for Exiting the European Union in the House of Commons on 10 October 2016.

Theresa May and David Davis have also announced a Great Repeal Bill, to be introduced by the Government into Parliament next year as the legal means to disapply the European Communities Act 1972, and all subsequent EU laws based on it. Under the Government's plan such Bill would only become the Great Repeal Act in 2019 after the UK has left the EU.

A court decision against the Government has the potential to change the timing of Brexit, should any resulting Parliamentary process extend beyond the Government's current deadline of triggering Article 50 by March 2017.

It remains likely that after this October's High Court hearing, the "Brexit case" will go on appeal to the Supreme Court for a final judgment in the New Year.