The launch of London's Night Tube on 19 August saw only four incidents occur - no more than on any previous start to the weekend - with 100,000 night time journeys completed during the weekend. Now Glasgow could follow.
Transport for London expects numbers to rise to around 200,000 per weekend as further lines open up.
Some 100 officers were on patrol but superintendent Chris Horton stressed that there was 'no reason' why passengers would not be as safe as during the day, and British Transport Police confirmed that no more incidents occurred than usual.
Trains now run regularly on the Victoria and Central lines on Fridays and Saturdays between 00:30hrs and 05:30hrs.
Outside London, the Strathclyde Partnership for Transport in Scotland has announced that is investigating the feasibility of extended hours on the circular Glasgow subway, once a £288m overhaul, currently under way, is complete.
Until now, running a regular after-midnight service has been impossible because of the amount of overnight maintenance needed to keep the 119-year old tunnels and 36-year old trains operational.
The Partnership acknowledges that later running would give an important boost to the city's £2.16bn night-time economy
Elsewhere in the UK however, the West Midlands Combined Authority and Transport for Greater Manchester, have no plans to announce comparable initiatives on their respective Midland Metro and Metrolink tram networks.
Similarly, in the Republic of Ireland, Dublin City Council is not contemplating an extended timetable for its Lucas light rail system.
