Most of the respondents to a poll on Tube opening times want a later weekend service, early indications suggest.
The Tube would open an hour later on Saturdays and Sundays
The Transport for London (TfL) survey, which asked if people wanted later services on Friday and Saturday nights, received more than 50,000 responses.
The move would mean tubes starting one hour later on Saturday and Sunday.
London Underground (LU) director Richard Parry said: "From the research we've done, we think there is a majority in favour of a later service."
But he said there was a "significant number of people" concerned at later start times on weekend mornings, including shift workers.
Mr Parry said LU believed "there are more people who would potentially use the service if it were to run later than would be able to in the mornings".
The two-month consultation, which ends on Friday, is the most popular in TfL's history.
If given the go-ahead, trains would operate on Saturday and Sunday until about 0130 BST - but would start later in the mornings.
The decision will be made later this year and any changes would be introduced in late 2006.
But London Transport Users Committee (LTUC) said the move would "seriously disadvantage early morning passengers such as shift workers".
Brian Cooke from LTUC said: "Many of these users come from low-income groups and travel longer that average journeys, for which there are no alternative forms of transport available."