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Erena Louise Wilson, 31, from Wellington, was walking through the gardens with friends on September 23 last year, when she was hit by a Lebanese cedar branch and suffered fatal head injuries.
It was raining and windy after a long dry spell just before the branch fell.
Tree branches are vulnerable to snapping off dropping off suddenly in such conditions known as 'summer branch drop', the Daily Mail reports.
However, Kew Gardens hadn't erected warning signs because it deemed the risk to be minimal, the Wilson family's lawyer, John McLinden QC, said.
It was a "fluke" the daughter of Ms Wilson's friend Tess Marshall was not also killed, Mr McLinden told an inquest at West London Coroner's Court.
The Mail reports that Ms Wilson, an accounts manager, was walking along a main path when Ms Marshall noticed a large branch, 6m long and 30cms thick, was crashing down from 18m above.
Ms Marshall screamed "run" and fled for her life.
"As I was running, I thought the whole tree was falling over. I was sure it was going to hit me. I was running away and then I heard a heavy thud. An oomph.
"I wasn't thinking, it was just instinct. I was just running."
When she looked back she saw Ms Wilson lying on the ground surrounded by tree debris.
Ms Marshall ran to her aid to find blood coming out of her ears and mouth, forming a pool of blood under her face.
Ms Marshall's brother gave CPR until paramedics and an air ambulance arrived.
But Ms Wilson suffered severe head injuries and was pronounced dead at 2.51pm after 45 minutes of cardiac resuscitation.
Last year, Ms Wilson's uncle, Pieter van Vliet, told the Mail the family wanted the issue of summer branch drop to be explored during the inquest to prevent further deaths.
"We're not experts but obviously Kew Gardens has trees, a lot of them, so potentially there is a good reason for bringing this up," he said.
The inquest continues.