A second man who died was named last night as Matthew Wood (39) from Sutton, south London, who is believed to have been walking to work.
Twelve other people were injured and police said it was a "miracle" more were not hurt.
The crash happened at 8am yesterday near Vauxhall Station when an AgustaWestland 109 Power helicopter hit a high-rise crane at The Tower, one of Europe's largest skyscrapers.
Mr Moule (31), a dad-of-two from Essex, was supposed to be at work at 7am with his colleague Mr Biagioni (30).
"It was the first time I've been late since starting this job three years ago. I just woke up late. Call it divine intervention if you like," Mr Moule said.
Mr Biagioni, also from Essex, was late because his four-year-old son, who usually wakes him up, slept in. His wife Leanna said he phoned her to say he should be dead. She said: "It's too horrible to think about."