Anita Trivedi's family fears she may have killed herself as a result of bullying at college.
A British Transport Police spokesperson said the death was not being treated as suspicious. An inquest into the death was opened on Wednesday and adjourned.
The 23-year-old student's father, Kailash Trivedi, a general practitioner, said his daughter had seemed happy despite repeating a year after failing a set of examinations.
"She was beautiful, very pretty, she cared for everybody. She was so good, so nice, so polite, so courteous. I miss her so much," he told The Times.
Anita returned home in east London from university last Wednesday morning distressed, having fought with a classmate after a seminar.
She was killed soon after by a train at Denmark Hill station, near the medical school campus.
Some said a member of staff had come into a class later to ask whether anyone knew what had happened.
Anita was believed to be upset about having to repeat a year but her father and tutors had reassured her that failing a year was relatively common among medical students.
"Our thoughts and deepest sympathies are with her family and friends and we continue to liaise with the coroner's office," a King's College spokesperson said.
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