Jacintha Saldanha, who has worked at the hospital for four years, was found at an address near the hospital.
The Two Australian DJs telephoned the King Edward VII Hospital and asked to be put through to the ward where Kate was being treated for severe morning sickness.
Miss Saldanha answered the call and put them through to the ward where the Duchess was being cared for, another nurse there updated them on her condition.
A Scotland Yard spokesman said: “Police were called at approximately 9.35am this morning to a report of a woman found unconscious at an address in Weymouth Street, W1.
“London Ambulance Service attended and the woman was pronounced dead at the scene. Inquiries are continuing to establish the circumstances of the incident.
“The death is not being treated as suspicious at this stage.”
London Ambulance Service said: “We were called at 9.25am to an address in Weymouth Street. We sent 2 ambulances crews and a duty officer, sadly the patient was dead at the scene.”
Michael Christian and Mel Greig, DJs on the 2DayFM radio station, broadcast their call to the hospital on Wednesday morning.
Miss Greig, who was impersonating the Queen, asked to speak to her “granddaughter, Catherine” and managed to persuade Miss Saldanha to put her through to the ward where Kate was being treated.
The King Edward VII Hospital released a statement which said: “It is with very deep sadness that we confirm the tragic death of a member of our nursing staff, Jacintha Saldanha.
“We can confirm that Jacintha was recently the victim of a hoax call to the hospital. The hospital had been supporting her throughout this difficult time.”
The Duke and Duchess of Cambridge said they were “deeply saddened to learn of the death of Jacintha Saldanha”.
The statement said: “Their Royal Highnesses were looked after so wonderfully well at all times by everybody at King Edward VII Hospital, and their thoughts and prayers are with Jacintha Saldanha’s family, friends and colleagues at this very sad time.”
The prank call was deeply embarrassing for the hospital, which is the medical institution of choice for the Royal Family.
Miss Greig and Mr Christian were lambasted on Twitter as news broke of the nurse’s death, with people calling for them to resign. Both have now shut down their accounts on the micro-blog site.
In the immediate aftermath of the call, the DJs apologised for the prank but later took to Twitter to brag of their success.
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