The crane operator only survived the Vauxhall helicopter crash because he was running late and had not reached his cabin when the aircraft came down, a witness said.
Lorry driver Paul Robinson, 42, said the man would have been "wiped out" if he had been on time this morning. Instead, he was still climbing up the crane's shaft when disaster struck.
Site workers said the man, who has not been identified, had never been late before. He is understood to have been held up while dropping his children at school.
Mr Robinson said: "He was halfway up to his cabin, he was making his way up by ladders when the helicopter hit.
"He would have been wiped out if he had been on time.
"It was a very lucky escape."
Robinson, a father-of-two from Dagenham in east London, said he was "100%" sure the man would have been killed if he had already been in position.
The crane operator, who had been harnessed to the structure, is now understood to be recovering from his ordeal.
Mr Robinson said he had been waiting in a queue to drive into the site when the crash happened.
As debris fell from the sky and hit the back of his lorry, he leapt out, believing another driver had bumped into him.
But as he looked up, he saw a "ball of fire".
He added: "I just ran. I panicked. My mind went blank and fuzzy.
"There was a ball of fire and someone said the helicopter had come down and hit the crane. It was terrifying."
Mr Robinson said he visited the site several times a week to collect waste.