British Transport Police says it is investigating the exact circumstances surrounding the deaths of the three men at Loughborough Junction, near Brixton, on Monday, June 18.
Two of the men were named on Tuesday, June 19, as Harrison Scott-Hood, 23, and Alberto Fresneda Carrasco, 19, who was born in New York but was a Spanish national.
"His absence has left a deep hole in the family," said a spokesman for his family.
Mr. Scott-Hood's parents Susie and Perry said their son was "loved by everyone" and had just returned from travelling in Vietnam and Cambodia.
"He was an intelligent and wonderful boy who had so many friends….he was a beautiful artist….Harrison completed us. He is irreplaceable," they said in a statement.
The third victim has not been named by police but the trio were known by their "tags" — Kbag, Lover and Trip.
'Revolutionary Artist'
Jim Jordan, who knew Harrison, said he had not been a hooligan but was a "gentle lad" from north London who saw himself as a "revolutionary artist".
He said he was shocked by some people's reactions on social media.