The Iberian plane appeared to ignore four warnings from air traffic control not to take off because doing so would put it in the path of the United Boeing 747 which was trying to land with hundreds of passengers on board.
A witness said: "The captain was told to stop four times."
The captain of the United 747 was forced to take evasive action, flying round the airport, before being allowed to land.
The CAA last night confirmed the incident had taken place. It had yet to call in the investigators, however.
It said the planes were a mile apart at the time and the air accident investigation board would not be examining the incident.
But sources at Heathrow said no official investigation could take place unless the CAA asked for it.
They said that investigators had shown an interest but were powerless to intervene unless invited to do so.
The incident shows up the increasing problems of takeoff and landing at Heathrow, particularly at busy times.
Industry sources said the incident showed that Heathrow was an extremely congested airport, and posed clear dangers to pilots on landing and takeoff.