The two men are believed to have been clinging to a British Airways flight from Johannesburg to Heathrow.
The victim was found on the roof of notonthehighstreet.com’s headquarters on Kew Road, Richmond, at about 09:35 BST on Thursday. Police said his death was being treated as unexplained.
The man who was injured is in a critical condition in hospital.
The Met Police said it could not confirm if the two cases were linked.
In a statement, the force said: “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 of enquiry into identifying the deceased and the circumstances of his death.”
The surviving man, who is believed to be aged 24, was found in the undercarriage of the plane at about 08:20 BST and taken to a west London hospital.
Officers believe they know his identity but are awaiting confirmation.
The 9,012km from South Africa to the UK usually takes about 11 hours.
In a statement, British Airways 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 the incident was “unrelated to the business or its team members and added the company was “co-operating with the ongoing police enquiry”.
A post-mortem examination will be carried out on the dead man, who has not yet been identified.
Officers said enquiries are ongoing into how long his body had been on the roof.
There have been other cases where stowaways have fallen to their deaths in London after smuggling themselves onto planes and hiding in landing gear.
In September 2012, Jose Matada, 26, died after falling from the undercarriage of a flight from Angola to Heathrow on to a street in Mortlake, west London.
An inquest heard he may have survived freezing temperatures of up to minus 60C (-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.-BBC