A number of actions have been launched attempting to prevent the government from formally triggering Brexit without Parliament's authorisation.
During the opening hearing, government lawyers told the High Court Prime Minister Theresa May did not intend to trigger Article 50 of the Lisbon Treaty before the end of 2016.
Article 50 begins the Brexit process.
A hearing in October will allow time for a possible appeal to be completed before the government seeks to leave the EU in line with the 23 June referendum result, the court heard.
The hearing will take place over two to three days.
Government lawyers are expected to argue that the prime minister can use historic Royal Prerogative powers to start the process of withdrawing from the EU, a course the challengers say is unlawful.
They say Parliament must give its authorisation.
The judges heard that one of the law firms involved, Mishcon de Reya, had received letters of abuse which led to potential clients who had wanted to join the action withdrawing their names.
"It is racist abuse, it is anti-Semitic abuse and it is objectionable abuse," Lord Pannick QC, instructed by Mishcon, told the court.
The judges ruled that the lead case in the action should be that of Mishcon client Gina Miller, 51, an investment manager and philanthropist living in London who voted Remain in the EU referendum.
Other applicants include London hairdresser Deir Dos Santos, 37, as well as Britons living in France campaigning as Fair Deal for Expats.
Mrs May has said she will not trigger Article 50 - which sets in place a two-year process for leaving the EU - until the end of the year.
The recently-appointed Brexit Secretary, David Davis, has said Brexit should be triggered "before or by the start of next year".
EU leaders have urged the UK to do so as soon as possible.
A legal challenge over the UK leaving the EU will be heard by the High Court in October, two judges have decided.