Alexia Walenkaki was being closely watched by her mother as she played with her friends on a rope swing in East London’s Mile End Park.
Speaking with The Standard, devastated mum Vida said: “She was playing with three other girls in the play area and just a few minutes before it happened, she came and sat on my lap and we were chatting.
“She had a drink and I told her we were going to leave in 15 minutes so not to go far.
A post-mortem is to be carried out today on Alexia, who was due to celebrate her sixth birthday on Saturday.
A joint investigation into the cause of Alexia’s death is being carried out by police and the Health and Safety Executive.
A spokesman for the Met Police said: “Officers and London Ambulance Service attended the scene and found a five year-old girl who was in cardiac arrest. At this early stage officers believe a tree fell on the girl.
“A joint investigation is being carried out into the circumstances of the incident by the Met’s Homicide and Major Crime Command and the Health and Safety Executive.”
Anyone who witnessed the incident should call police on 020 8345 3715.