Remainers struck an optimistic note despite Scotland's highest court delaying a decision on whether to sign a letter requesting a Brexit extension if Boris Johnson refuses to do so.
A small number of protesters brought signs and flags as they awaited a decision.
Elaine Motion, acting on behalf of the petitioners, said there was now a "Damocles" hanging over Prime Minister Boris Johnson's head if he refused to comply with the law.
"For the first time ever in these answers the prime minister had to confirm that he would abide by the Benn Act, which he had refused time and time again before all of you to concede," she added.
Motion's clients include prominent anti-Brexit campaigners SNP MP Joanna Cherry, businessman Dale Vince and Jolyon Maugham QC.
Legislation passed by Parliament in September, known as the Benn Act, requires the prime minister to ask for more time if there is no Brexit deal in place by October 19.
The government has given assurances that it would follow the terms set out in the Benn Act.