Officers at the Metropolitan Police are appealing to witnesses following the incident onboard a number 13 bus on December 28.
Emergency services were called at 12.35am last month with reports of an elderly woman having taken ill just after boarding the bus.
The 78-year-old had suffered a cardiac arrest and was taken to hospital where she later died on January 4.
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The woman’s family are being supported by a specially trained officer whilst the circumstances that led to her death are investigated.
The driver of the bus is assisting police with enquiries and there has been no arrest.
Anyone who was on board the bus at the time of the incident but left prior to the arrival of police, and who could assist police is asked to call 101 or ‘X’ @MetCC and quote CAD2686/28Dec.