Two aircraft were at serious risk of colliding as they came within 100m (328ft) of each other in mid-air, a report found.
A Falcon 2000 plane and a Glasflugel Mosquito glider had the near-miss north of Haverhill, Suffolk on 5 September.
The pilot of the Falcon said there was "no time, nor need" to take action as "the threat was gone within seconds".
But the UK Airprox Board said it was "entirely serendipitous" that there was no collision.
It classed the risk of collision as A, its highest category.
According to the report, the pilot of the Falcon plane said the near-miss happened while the "Cambridge controller was busy attempting to obtain a concise position report from a glider which had reported approaching the airfield".
It added: "It was during this conversation that the Falcon pilot had an Airprox [incident] with another glider which was not working the Cambridge frequency and which did not appear to have any collision avoidance equipment."
The Mosquito pilot is reported as saying they had "spotted, in the corner of their eye, an aircraft passing to their right, coming from behind them and travelling very quickly".
When the the Cambridge controller was told of the near-miss he believed "the Falcon pilot was wrong", said the report.
The Airprox Board concluded it had been "a very close encounter" where the most viable of its recognised safety measures "had been 'See and Avoid', which had ultimately been found to be ineffective".
The board said "a serious risk of collision had existed because the separation that had been present had been entirely serendipitous".