The A320 plane was descending toward Heathrow Airport in July when the drone was spotted from the cockpit window, according to the UK Airport Board report.
The plane was flying at an altitude of 4,600 feet (1,402 meters) near the Shard skyscraper in central London when the 50-centimeter (19-inch) drone was spotted.
A "very near-miss"
The pilot said the risk of collision was "high" in the report released last Friday. The authors of the report also classified the incident as a "very near-miss" and said that "chance had played a major part."
They added that the drone operator could not be 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.