Ellie Burrows, Southeastern’s train services director, said: “The closures mean we are unable to run our normal service and it will mean considerable disruption for our passengers, particularly for those four working days.
“We are doing everything we can to provide alternative journey options, and we’ll be running longer trains where possible.
“But with the three major London stations closed there will be fewer services, queues are to be expected and trains that do run will be very busy.
“We’ve been working very closely with Network Rail, TfL and the Department for Transport to plan for this and we’ve been giving passengers advance notice so they can plan ahead.
“We urge passengers to check how their journeys will be affected by visiting our website.”
Those trains that do run in the period affected will be much busier than usual and will be diverted to other stations, including Victoria, Blackfriars, Cannon Street and London Waterloo International.
Queuing systems will be in place at some stations and passengers are advised to leave more time for their journey.
The rail franchise has revealed it will also have to halt some late-night services at the end of this month.