The proposed change would allow trains to run later on Friday and Saturday nights, but could affect more than 50,000 early morning users. Trains would arrive at central London stations at around 7am on Saturdays and 8.30am on Sundays.
TfL will target people on its Oyster database, sending emails to those who have supplied addresses and direct mail to those who have not.
The campaign also includes above-the-line media such as Tube posters and press ads in Metro, regional and ethnic newspapers. Leaflets will be available in all stations and handed out by staff where morning Tube traffic is highest, and to night bus users around Trafalgar Square and taxi users on Cranbourne Street on Friday and Saturday nights.
An inbound contact centre will provide a helpline to fulfill information and questionnaire requests.
Mike King, group marketing communications manager at TfL, said that the benefit to late night users needs to be weighed against people's need to get to work on time in the mornings.
"Before we make a decision we want to make sure our regular customers' views and needs are taken into account, and we're confident that this campaign will give us a big response across the board," he said.
The campaign will run until April 22.
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