The plane narrowly avoided colliding with a drone while flying near The Shard, London's tallest skyscraper, as it approached Heathrow Airport on July 18, was within 66ft (20m) of the device, according to the UK Airport Board report.
The report, based on the pilot's observations, described the incident as a "very near miss".
The plane was at an altitude of 4,900ft (1,494m) when the drone was seen from the right-side flight deck window.
The report said: "Members agreed that this incident appeared to be a very near-miss and that the drone operator should not have been flying in that location at that altitude."
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It added that the account of the incident "portrayed a situation where a collision had only been narrowly avoided and chance had played a major part".
The incident was deemed to be in the "most serious" category of risk. The drone operator has not been traced.
The incident is one of dozens of near-misses reported to the UK Airport Board each month.
In a separate incident, also in July, a drone came within five meters (16 feet) of an A319 passenger plane taking off from Britain's Liverpool Airport.