On 13th, 17th and 18th October 2016 the High Court heard the cases of R (Santos) v Secretary of State for Exiting the European Union and M v Secretary of State for Exiting the European Union. The court composition was the Lord Chief Justice, Master of the Rolls and Lord Justice Sales.
A very welcome development was the publication of transcripts of the proceedings - see Courts and Tribunals Judiciary website.
The issue in the case was stated by Lord Pannick QC (Counsel for Gina Miller) - "Can the defendant, on behalf of the government, lawfully use prerogative powers to give a notification under Article 50 of the Treaty on European Union of this country's intention to withdraw from the EU."
The court will give judgment in the near future.
UK Constitutional Law Association Blog - Robert Craig - Report on the proceedings 13th October (i.e. the first day of the hearing) and On the Second Day of the Hearing and On the Third (and final) Day of the Hearing. Note: the Association's blog has numerous articles on many aspects of "Brexit."
Jolyon Maugham QC - Financial Times 14th October - The Article 50 challenge shows parliament should have its say. Also see, by the same author, A whine from sour grapes.
Michael Zander QC - New Law Journal - Oral arguments in the Art 50 court case
New York Times - Without a Constitution; "Bexit" is guided by a prerogative. But whose?
UK Constitutional Law Group - Piet Eeckhout - The UK decision to withdraw from the EU: Parliament or Government
My view of 27th June and links to views of other commentators