The incident was reported between Clapham Junction and Twickenham at around 5pm today (April 21).
National Rail confirmed that all lines between these stations have closed and services may be delayed by up to 15 minutes.
It has affected South Western Railway services at London Waterloo with disruption to last until 10pm.
All power on the tracks has been turned off as the incident is dealt with by emergency services.
The nature of the incident is unknown at this stage.
We have contacted British Transport Police and London Ambulance Service for further information.