The plane, with up to 215 passengers plus crew on board, avoided disaster by seconds in the near-miss at 4,000ft last September.
It is illegal to fly unmanned aircraft at more than 400ft without special permission.
But this was one of seven incidents in which drones flew too close to planes, says an alarming report by the UK Air Proximity Board.
Now airline pilots, fearing a "catastrophic crash", are calling for a clampdown.
Another rogue drone almost hit the wing of a Boeing 777 taking off from Heathrow last September. The pilot said it flew down the right-hand side of his plane at 2,000ft, leaving him no time to take avoiding action.
The Air Proximity Board said "chance had played a major part" in avoiding a collision.
Two other serious or Category A near-misses were at London City airport and Manchester. The pilots' union Balpa has called for drones to be made visible on radars and wants stricter rules and a registration system so errant operators can be traced and prosecuted for 'irresponsible flying.'
Balpa fears the number of incidents could rise as people begin using drones they have received as Christmas presents.
Spokesman Steve Landells said: "We must act now to protect passengers and flight crew and make sure a catastrophic crash does not happen. Anyone flying a drone must do so in a safe and sensible way."
The report comes after the Oxford Research Group warned that drones could be used by terrorists as "simple, affordable and effective airborne improvised explosive devices".
Drones or "unmanned aerial vehicles" can reach heights of nearly 20,000ft and often have cameras that let the "pilot" on the ground to see the view from the air. Prices vary from less than £20 (NZ$44) to as much as £4,000 (NZ$8,795).
A spokesman for the UK Civil Aviation Authority said: "Drone users have to understand that they are potentially flying close to one of the busiest areas of airspace in the world.
"The rules for flying drones are designed to keep all airspace users safe and anyone flouting these rules can face severe penalties including imprisonment."
The Department of Transport said: "The Government is leading efforts with international bodies to develop a stringent regulatory framework focusing on safety."
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