More than 20,000 people have responded in the first 48 hours to a poll on whether Tube services should run an hour later on the weekend.
The Tube would have to open an hour later
The public can register their views on the Transport for London (TfL) website.
A TfL spokesman said: "This may turn out to be the most popular public consultation ever undertaken by Transport for London."
He said research had shown "clear public support for the Tube to run for an extra hour on Friday and Saturday".
But TfL has warned a later-running Tube would mean the service would have to start an hour later on Saturdays and Sundays to allow "essential maintenance to track, trains and signals".
It said while later running trains "may benefit an estimated 140,000 extra passengers each weekend with their journey home, there are an estimated 55,000 people that could be affected".
The delayed closing of the Tube on both nights would mean later start times of 0700 GMT on a Saturday and 0830 GMT on a Sunday.
People wanting to make submissions have until 22 April to pick up leaflets at any Tube station, or go to the TfL website or send e-mail messages to firstname.lastname@example.org.