The claimants succeeded in their argument that Article 50 may not be triggered without the further involvement of Parliament. So held the High Court in M and Santos v Secretary of State for Exiting the EU. See the court's full judgment via Bailii.
Previous post with links to the transcripts of the 3 day hearing -High Court hearing on article 50 litigation.
It is to be noted that the government (via its lawyers) accepted that the matter was a proper one to be heard by the courts and the court was at pains to point out that they were not saying anything about the merits or demerits of a withdrawal by the UK from the EU. At para. 5 of the judgment, the court said:
"It is agreed on all sides that this is a justiciable question which it is for the courts to decide. It deserves emphasis at the outset that the court in these proceedings is only dealing with a pure question of law. Nothing we say has any bearing on the question of the merits or demerits of a withdrawal by the United Kingdom from the European Union; nor does it have any bearing on government policy, because government policy is not law. The policy to be applied by the executive government and the merits or demerits of withdrawal are matters of political judgement to be resolved through the political process. The legal question is whether the executive government can use the Crown's prerogative powers to give notice of withdrawal. We are not in any way concerned with the use that may be made of the Crown's prerogative power, if such a power can as a matter of law be used in respect of Article 50, or what will follow if the Crown's prerogative powers cannot be so used."
It has been announced that the government will pursue an appeal to the Supreme Court. The government could have chosen to take the matter to Parliament and avoid further delay as well as the possibility that the Supreme Court might refer to the Court of Justice of the EU the question whether notice under Article 50 may be revoked unilaterally by the member state. Further delay may well be seen as economically damaging.
Before the High Court, perhaps for purely tactical reasons, it was assumed by all parties that an Article 50 notification could not be unilaterally withdrawn by the UK once given. There is respectable argument to that effect but others doubt that it is correct. The only way to obtain a definitive answer will be for a reference to be made to the Court of Justice of the EU. Even if notification can be withdrawn, the problems of doing so could, in practice, be difficult. Those problems seem likely to increase the longer the period that elapses before the withdrawal.
On 28th October, the High Court in Northern Ireland (Maguire J) found for the government in relation to a number of issues specific to Northern Ireland - The High Court of Northern Ireland - a very brief note on the Brexit case. The court put a number of other matters "on hold" pending the outcome of the High Court hearing in London.
Given that the Parliamentary Briefing on the Referendum Bill is referred to in the judgment (para 107) it is worth reading since page 25 makes it clear that the Bill would establish a consultative referendum. Legal opinion is beyond doubt that the Referendum Act 2015 itself contained nothing to bind anyone in law to do anything. This contrasts markedly with the Alternative Vote (AV) referendum where the legislation placed a duty on the Secretary of State to implement the result had it been in favour of AV.
The case divided legal opinion but this outcome accords with my own preferred view as expressed on this blog a few days after the referendum - post of 27th June 2016. In a post on Head of Legal blog published 4th November, Carl Gardner explains why he thinks the High Court decision is wrong though he doubts that the Supreme Court will reverse it - Why the High Court got the law wrong about Brexit. I am expecting there to be a considerable amount of comment on this case and I will endeavour to keep abreast of it and will post links to this blog.
The Spectator - Brexit means defending UK laws and courts.
The following are (mostly short) articles in which the various authors give their reaction to the judgment:
Paul Daly - Administrative Law Matters - Some thoughts on R (Miller) v Secretary of State for Exiting the EU  EWHC 2768.
Prospect - What does today's High Court ruling on Article 50 mean?
David Allen Green - Financial Times (£) - The Article 50 decision is taken out of Theresa May's hands
LSE - Jo Murkens - The High Court ruling explained: An embarrassing lesson for Theresa May's government.
Queen Mary University - Professor Sionaidh Douglas-Scott responds to Brexit judgment
How to Crack a Nut blog - Albert Sanchez Graells - Why an appeal of the High Court Parliamentary Approval Brexit judgment will bring the litigation to the Court of Justice of the EU
EU Law Analysis - Steve Peers - Brexit: can the ECJ get involved?
Liverpool University - Viewpoint: Legal analysis of today's successful; Article 50 challenge
Barrister Blogger - Rushed, barely coherent thoughts on today's Article 50 judgment
The Justice Gap - Brexit means Brexit (subject to parliamentary approval)
Spinninghugo - How the government lost
Verfassungsblog - The High Court judgment in Miller and others: Four brief remarks
Rightsinfo - Breaking: Government loses Brexit trigger challenge
Steve Cornforth blog - The Brexit judgment is all about the supremacy of our elected parliament
Public Law for Everyone - Prof. Mark Elliott - The High Court's judgment in Miller: A Brief Comment
Greg Callus - A Typo in the Constitution blog - After the Miller judgment
Judicial Power Project - High Court Miller Judgment: Expert reactions
Jamie Foster - Brexit gunpowder treason and plot