Police were called by the London Ambulance Service to an address in Lansdowne Crescent shortly after 2.25pm on Monday October 29 following reports of an injured infant.
On arrival, officers found a two-year-old girl who was treated by paramedics and taken to a west London hospital. She was pronounced dead at 3.17pm.
A post-mortem at Great Ormond Street Hospital is scheduled to take place in due course.
The spokesman said a woman, believed to be the toddler's mother, was taken to hospital and treated for shock.
Officers from Kensington and Chelsea CID are investigating the incident. At this stage it is being treated as non-suspicious.
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The 38-year-old victim was standing on a busy Victoria Line train when another passenger approached him.
The boy, called Roman, told police call handler his mum "is dead" and "she's closing her eyes and not breathing".