Britain's Prime Minister Boris Johnson talks with prison staff during a visit to HM Prison Leeds, in Leeds, Britain August 13, 2019.
A judge has set the date of Friday 6th September after an initial hearing earlier.
Johnson says Britain will leave the European Union on October 31, with or without a divorce deal.
Johnson has drawn criticism for pledging to leave with or without a trade agreement with the EU.
They have been investigating what parliamentary procedures can be used to prevent such an outcome, and in July backed proposals to make it harder for Johnson to force through any departure without a deal.
In June, House Speaker John Bercow said it was "blindingly obvious" that the prime minister could not sideline parliament.
"That is simply not going to happen", he said.
More than 70 MPs and Peers are backing the bid, which would make it "unlawful and unconstitutional" for the Prime Minister to prorogue parliament and force the United Kingdom to leave the European Union without a deal in place.
Mr Johnson has made a "do or die" pledge to exit the bloc in 79 days time and has refused to rule out proroguing parliament to honour the result of the 2016 referendum - despite huge opposition from MPs.
It has been suggested that in order to achieve a no deal Brexit, Johnson could decide to close parliament in the run up to the deadline.
Brexit opponents say a no-deal divorce would bring disruption at borders and cause significant economic damage, tipping Britain into a recession.
Ms Abbott, asked if Labour is planning to move a vote of no confidence against Mr Johnson's Government in the first week of Parliament's return, said: "It's above my pay grade to say when we'll move the vote of no confidence".
Anti-Brexit campaigners have already enjoyed success in the courts.
Numerous pro-EU MPs who are bringing backing the case are the same MPs who won the case at the European Court of Justice to allow the United Kingdom to evoke Article 50 at any time and remain in the EU without the permission of the other 27 member states.