A British Transport Police (BTP) spokesman said:
"BTP officers were called to Riddlesdown rail station in Purley on Friday, 22 March after a report that a woman and a child had been struck by a train.
"The incident was reported to BTP at 8.29am and was also attended by Metropolitan Police officers.
"Medics from the London Ambulance Service also attended, but a woman and a child were declared dead at the scene.
"The station has been temporarily closed while officers and medics deal with the incident.
"Enquiries are ongoing to establish the circumstances, and a file will be prepared for the Coroner."