The pilots “remained in constant visual contact” with the gadgets to ensure they did not hit the airliner as it passed alongside them, according to a report by the UK Airprox Board (UKAB).
There would have been a “significant risk of collision” if the passenger jet was on a different approach path to Heathrow, according to one of the pilots.
A report was made to the Metropolitan Police but the drone operators could not be traced. It was estimated that the drones came within 500 metres of the aircraft, which was not identified in the report.
The Civil Aviation Authority (CAA) said the incident on November 20 last year was the first aircraft near-miss involving more than one drone.
Less than half an hour later, a Boeing 777 approaching Heathrow flew within 50 metres of what is believed to be one of the drones. The pilot saw an object that was white, around two metres wide and with four prongs.
There were five near-misses between aircraft and drones in the latest monthly UKAB report, bringing the total over the past 12 months to 62.
Earlier this month, an investigation revealed that police are being flooded with reports about drones after a dramatic surge in incidents registered by forces, including rows between neighbours, prison smuggling, burglary “scoping” exercises and snooping fears.
Figures obtained by the Press Association showed forces recorded 3,456 episodes last year, almost triple the 2015 figure of 1,237 and more than 12 times the 2014 tally of 283.
CAA rules state that drones must not be flown above 400ft or near airports or airfields.
In November it launched a website to publish its revised code of conduct for drones, called the Dronecode.
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