Face of Nation : The train partly left the tracks at low speed outside Victoria station at about 03:00 BST.
No Gatwick Express trains are running, while Southern warned its services would be “severely reduced”.
Network Rail said it was working to remove the train but passengers should “travel later in the day if possible” or seek an alternative route.
The train is stuck across a number of tracks meaning platforms nine to 13 at Victoria have been blocked, while services are not able to use the “slow/stopping” lines to and from Clapham Junction.
Some trains are also unable to leave the Battersea depot, so further reducing the number of services that can run.
Recovery teams have cut the 50 tonne train from its two wagons and are lifting it back on to the track using hydraulic jacks.
Network Rail said the work will not be completed in time to run a full evening rush hour service although it hoped the obstruction would be removed by 17:00 “if all goes to plan”.
Trains running through Gatwick Airport have also been disrupted by a separate signalling fault and a passenger who was injured as they left a carriage, which led to one platform becoming blocked.
Some commuters took to social media as they found their trains had been cancelled.
Other stations, including London Bridge, also became congested as people tried to find alternative routes.
A Network Rail spokesperson said passengers should travel “via London Bridge or London Blackfriars as trains will be delayed, diverted or cancelled”.
The spokesperson added that once the engineering train was removed from the tracks there would be a “full investigation to understand how it happened.”
Train tickets for Southern and Gatwick Express services are being accepted for reasonable routes on other services.
Disruption is expected to last throughout Tuesday.
