Their four-year-old son Romeo apparently has epilepsy and the flashlights can trigger an attack.
Victoria revealed this last week when she and Romeo were confronted at Heathrow Airport by photographers who were snapping away as they walked to a waiting car.
Photos that were published in the News of the World on Sunday showed the little boy covering his eyes as the lights flashed.
They pushed through the photographers and were sitting in the car when a final flashlight caused the boy to shout and cry.
His visibly upset mother shouted: "He has epilepsy, all those flashes will set off an attack, you can't do this."
The newspaper said the Beckhams had only recently discovered that their second eldest child had epilepsy, after he had suffered fits and was rushed to hospital four times.
A friend of the Beckhams said: "They are devastated - worried sick about Romeo. He is on medication to control the seizures but obviously things like flashing lights can trigger one at any time."