The report blamed the "inappropriate actions" of the air traffic controller for the incident in which the British Airways jet almost landed on top of a British Midlands Airbus which was waiting to take off.
The planes were a split second away from disaster and an accident was only averted when the British Airways pilot suddenly noticed the Airbus while heading towards it at 150mph.
Yesterday, aviation experts warned that the increasing volume of planes using Heathrow - described by one pilot as "the most dangerous place to land" - meant a fatal accident was "just waiting to happen".
The report, by the government-funded air accidents investigation branch, which normally investigates accidents, not near misses, revealed that an air traffic control trainee, who was a third of the way through her course, was controlling take-offs at the time but made no criticism of her performance. Instead, it condemned her supervisor for allowing a "hazardous" situation to develop.
It added that this mentor should not have been chosen since he was involved in a similar incident in April 1999, in which he cleared a Boeing 757 to cross the runway in front of a Boeing 747. He has since been transferred out of Heathrow to a "less busy" airport, and is no longer involved with training.
His employer, national air traffic services, has introduced a more formal system for selecting trainers and for monitoring individual performance - two key recommendations of the report.
The AAIB report found that the Brussels-bound British Midlands Airbus A321, with 89 passengers on board, had begun to taxi down the take-off runway on April 28 as the British Airways 747 from Tokyo, was given permission to land in the same place shortly before 2pm.
With bad visibility, the pilot of the BA plane failed to notice the British Midland - now bmi - jet as it came through the clouds, and only glimpsed it from a distance of about half a mile.
As he began to take action, aiming to "go around" - veering away directly above the smaller plane - the controller spotted the problem, ordered the British Midland plane to stop taxiing and the BA jumbo to pull away. The BA pilot's quick thinking meant he could do so, but at this point the BA plane was just 112ft away - less than twice its own height.
Last night, Keith Williams, a spokesman for Nats, insisted that, at an airport with 460,000 aircraft movements a year, this was the "only serious safety-related incident". But he conceded: "It is one too many."
Aviation industry experts - who have described it as the closest near miss in the 30 years since jumbo jets started flying to Britain - warned that such near disasters would happen more frequently unless the government acted to curb congestion at airports, now "close to capacity", and recruit and train more controllers.
"If controllers continue to be pressured to take on more and more then there will be more and more near accidents," said Iain Findlay, aviation officer for the Institution of Professionals, Managers and Specialists, the air traffic controllers' union.
One BA 747 pilot said the overcrowding at Heathrow was so extreme the airport was notorious among the aviation community as the most dangerous place to land.
With planes landing and taking off within 90 seconds of each other on two runways, he explained: "The spacing is down to the absolute minimum. It's almost routine to be told to expect a very late landing clearance ... which means you have just a few seconds to avoid a plane on the Tarmac ... and it's fair to say an accident's just waiting to happen.
"The controller has taken the blame but it's not really his fault. Planes are coming in so fast, controllers have to trust pilots can get off in time. The problem is, if they push their luck too much, something like this can happen."
