Two men found dead on the train tracks had been riding on top of a freight train wagon, police said.
Officers were called to the line between Hackney Wick and Stratford in east London in the early hours of Thursday.
British Transport Police said a 27-year-old man from Clerkenwell and a 25-year-old man from Aberystwyth suffered severe electrical burns and died.
Their next of kin were being supported by family liaison officers, it added.
Det Sgt David Taylor said officers had worked throughout the night to understand what had happened to the men.
He added: "The initial evidence that we've been able to gather suggests that both men were on top of a moving freight train wagon when they came into contact with the overhead power lines."
On Thursday, a police spokesman confirmed they were investigating whether the victims were graffiti artists or possibly "train surfers".
But Det Sgt Taylor said: "Our investigation will continue to examine how and why they came to be on top of this train although there is nothing to indicate that graffiti was involved."