The proposals would see tubes running until 2am on Friday and Saturday nights from 2015.
Current services run from round 5am to shortly after 1am.
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Police believe the 'vulnerable' two-week-old baby was being concealed to stop him going into local authority care.
A woman believed to be originally from north London was one of the nine people shot by Oregon college murderer Chris Harper-Mercer.
Detectives believe the boy's mother and family members are deliberately concealing the baby, and may be committing an offence.