Two Heathrow-bound Boeing 757s were in a "stack" of airliners awaiting landing instructions, when one was ordered to descend - into the path of the other.
Fortunately, the pilot of the higher of the two planes spotted the danger and climbed to safety as the aircraft came within 400ft of each other.
The pilot who took evasive action said there had been "a high risk of collision" and that one would have occurred if the weather over Biggin Hill in Kent had not been good.
In a report on the incident, on 22 November last year, the Joint Airprox Working Group - which studies aircraft near-misses - said it had been a "very serious" incident.
One military member of the JAWG expressed "surprised that neither pilot felt the necessity to query the controller's instructions", adding that "the old adage 'don't assume, check' was still valid".
Air traffic control procedures are now being looked at. One jet was at 10,000ft while the other was 1,000ft higher, and so close that the air traffic controller could not read their overlapping identity tags on his radar screen.
The controller wanted the lower jet to descend to 9,000ft, but mistakenly gave the order to the pilot of the higher aircraft, who descended 600ft in 30 seconds before climbing to safety.
"Had it not been for the excellent daytime visibility, which enabled the [higher] pilot to ensure visual separation was maintained, a more serious incident might have resulted," said the report.
Both Boeing 757s were British Airways aircraft. The higher of the two planes was flying in from Orly airport, Paris, with 165 passengers on board and seven crew. The other 757 was en route from Geneva and was carrying about 150 passengers.
Figures show that from September to December last year, there were 13 "near-misses" above Britain involving commercial aircraft. This was three less than the comparable period in 1995.
The incident, experts said, would not have happened in the United States. There, aircraft are fitted with traffic collision avoidance systems, which warn pilots of approaching aircraft.Reuse content