Transport police and paramedics were called at around 11.40, but despite treatment the 30-year-old man from Hampshire was pronounced dead at the scene.
Two other workers who were nearby are not thought to have been hurt.
Andrew Haines, Network Rail chief executive, said: “I am devastated to confirm that a colleague has lost his life following a tragic accident near Surbiton today. This is an incredibly sad time for the railway family.
“My thoughts, and those of everyone at Network Rail, are with the families and friends of the colleague involved. Our immediate priority now is to cooperate fully with the British Transport Police and Rail Accident Investigation Branch to fully understand what happened.”
TSSA General Secretary, Manuel Cortes, said: “It would be wrong to speculate at this time about what has gone wrong, but a full and thorough investigation must take place, so lessons can be learned.
“Our union has been warning Network Rail about the alarming number of near misses and fatalities we have seen over the past year.”