Scotland Yard was informed after the incident in November last year, but the drones' operators have not been found, a report by the UK Airprox Board (UKAB) said this week.
The UK's Civil Aviation Authority (CAA) said it was the first time a near-miss incident involving more than one drone.
The incident occurred over east London as an Airbus A320 was approaching Heathrow Airport on November 20 last year.
The UKAB report concluded that the incident had "compromised the safety of the aircraft".
"The board considers that the drone operator had endangered the A320 and its occupants," the report said.
One pilot also said there would have been a "significant risk of collision" if the jet had been on a different approach path.
The plane was flying at 5,500 feet when its crew spotted two white, orb-shaped drones nearby.
The pilots "remained in constant visual contact" with the gadgets, which are estimated to have got as close as 500 metre to the aircraft, according to the report.
Less than 30 minutes later, a Boeing 777 approaching Heathrow flew within 50 metre of what is believed to have been one of the drones, described as white, about 2 metre wide and with four prongs. It was believed to be one of the drones spotted earlier.
According to the UKAB's monthly reports, there have been five near-misses between aircraft and drones in March, bringing the total to 62 over the past 12 months.
Under CAA rules, drones must not be flown above 400 feet or near airports or airfields.
Last year, more than 3,456 incidents involving drones were recorded, compared to only 1,237 in 2015. The incidents include invasions of privacy, disputes between neighbours and prison smuggling.
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