Donna Oettinger, 41, and her son, Zachary, 3, were pronounced dead at the Riddlesdown station in Surrey, The Independent reported. Witnesses said Oettinger stepped from the platform to the track as a rush-hour train approached the station.
Commuters said many of those waiting on the platform did not realize what happened until they were ordered to leave the area.
James King, who was on the London-bound train, said passengers learned what had happened from Twitter, although the engineer got on the public address system asking for the conductor and sounding "panicked."
Few details were released about Oettinger. The Independent said she posted emotional messages on Facebook last year about her son.
"Thank god I have my son zaki I owe him a lot when I get better love you son with all my heart xxx," she said.
In another, she said: "Best day of my life when my beautiful zaki was born he brings so much happiness to my life."
Rail service on the line from Uckfield to London Bridge was suspended for several hours.