A suspected fire on the tracks is causing delays on trains travelling between Motspur Park and Chessington South.
South West Trains, which operates along the line, tweeted that the Chessington line was closed as there was believed to be damage to the rails and something smouldering on the tracks.
A spokesman for Network Rail said: “We have people on site looking at it and looking to see if we will be able to run trains over the damaged section of track as soon as possible.”
He said only the last three stations on the line were affected as trains could not get through.
A train is currently being held at the platform of Morden Manor station.
Network Rail was called to investigate the problem at about 3.40pm this afternoon. Passengers are advised to check the Network Rail website to plan their route.