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.
More top news
Nice work if you can get it?
Fagan-Gayle, a singer song writer who has also appeared on Celebrity Big Brother.
Police were called at around 2.30am on Wednesday and found sledge hammers and pick-axes.