Two men are believed to have clung on to a British Airways plane as it flew more than 8,000 miles (12,875km) from Johannesburg in South Africa to Heathrow.
The victim fell on to the roof of the business NotOnTheHighStreet.com in Kew Road, Richmond, south west London, yesterday morning.
Police and ambulance crews found the man dead at the scene at around 9:30am.
It is understood the second man, believed to be aged between 25 and 30 years old, was found unconscious in the undercarriage of the plane at Heathrow around an hour earlier.
He was taken to a west London hospital where police say he remains in a critical condition.
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.”
Hady Khoshkbary, who runs a printing shop next door, said he spotted police cars and ambulances outside yesterday morning and went out to discover what had happened.
He said: “We were very lucky that the body did not drop on the road, it dropped on the building.
“We were very, very lucky that we did not see the body. Already this is a tragedy but that would have been horrific to see.”
The Metropolitan Police said officers are investigating the death and whether the dead man is a stowaway.
They said: “The body is so far unidentified and inquiries 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 inquiry 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 second man was rushed to hospital where he was in a serious condition, but police said this has now deteriorated and he is “critical”.
Heathrow officers believe they know the man’s identity, but are waiting for confirmation before releasing any details of his nationality.
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.
“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.”
Tributes to the dead stowaway have been outside the building where his body was found after plummeting from the jet.
A single bunch of yellow freesias was laid at the entrance to the online gift business.
Business owners and staff spoke of their shock and have told how others had plunged to their deaths nearby under similar circumstances in recent years.
A member of staff at nearby Molly’s pub said: “It happens all the time. There was one on the Upper Richmond Road in Sheen five years ago.
“He landed in the street and just exploded. It was horrific. It’s just part and parcel with living around here for some reason.”
Speaking of yesterday’s horror, she added: “It’s very upsetting and it’s dangerous.
“He could have hit a car or a small child and killed someone else.
“Every single plane should be checked and double checked.
“I know they do get checked, but there must be a gap in there somewhere.”
Charles Campbell, 59, a carpenter from Ealing in west London, left a bunch of yellow flowers.
He said he was moved to bring the flowers because he thought no-one else would.
“He’s got a family and it’s Father’s Day Sunday. This is not first time his has happened,” he said.
Nazeer Fawad, owner of kebab house Yummy Bites on the same road, said: “I heard about it this morning. He was trying to save his life but unfortunately he lost his life. I just feel so bad.”
Mr Fawad, 41, who came to the UK from Afghanistan in 1999, added: “I think it must be they had a really tough time in their own country, so if you’re not happy in your house you’re looking to leave.
“I came by road, not air, and I’ve seen a lot of bad things in my life, and it’s my luck to be here talking to you. He was one of the unlucky ones.”
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 – a ten minute drive away from this latest incident.
An inquest into his death heard the young man from Mozambique is believed to have survived freezing temperatures of as low as 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.