A Scotland Yard spokesman said: "On Thursday 18 June police were called at around 09:35hrs to reports of a body discovered on the roof of a business premises on Kew Road, Richmond.
"The body is so far unidentified and enquiries are ongoing into this and how long it had been at the scene. No next of kin have yet been informed.
"At this time there is no evidence to link the death to the discovery of a stowaway in the undercarriage of a plane at Heathrow Airport; however this is one line enquiry into identifying the deceased and the circumstances of his death.
"The death is currently being treated as unexplained. A post-mortem examination will be held in due course."
The spokesman added: "At around 08:30hrs earlier that day, police at Heathrow Airport were called to reports of a suspected stowaway on a flight from Johannesburg to Heathrow.
"The man, believed aged 24, was found in the undercarriage of the plane and was taken to hospital. His condition is now described as critical.
"Whilst Heathrow officers believe they know his identity they await its confirmation before releasing any details of his nationality."
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Reverend Neil Summers, from the St John the Divine of Richmond church opposite where the body was found, said he was "shocked" and would lead prayers for the dead man.
He said: "It's shocking, you do not expect these things to happen on your patch really.
"In one sense it's not totally surprising as it's happened before.
"It's very shocking when it's so close to you.
"We are going to say prayers for the people concerned tonight."
A British Airways spokeswoman said: "We are working with the Metropolitan Police and the authorities in Johannesburg to establish the facts surrounding this very rare case."
NotOnTheHighStreet.com said in a statement: "Officers and the London Ambulance Service attended and found the body of male on the roof of the premises.
"The death is currently being treated as unexplained but early indications are that the body may be that of an airline stowaway."
They said the incident "is unrelated to the business or its team members" and they are co-operating with the police inquiry.
While rare, there have been other cases when stowaways have plunged to their deaths in the leafy streets of west London after smuggling themselves on to planes.
They hide themselves in the landing gear where they are exposed to the elements and have to endure plummeting temperatures. Most are killed by the cold and lack of oxygen at high altitudes.
In September 2012, Jose Matada, 26, died after falling from the undercarriage of a Heathrow-bound flight from Angola on to a quiet street in Mortlake, west London.
An inquest into his death heard that the young man from Mozambique is believed to have survived freezing temperatures of up to minus 60C (minus 76F) for most of the 12-hour flight.
But it was believed he was "dead or nearly dead" by the time he hit the ground.
