A Multiplex spokesperson said that the importance of safe working practices had been underlined to all workers on the site.
He said: "The site was shut for a day but is now back up and running. It is a very sad accident and our thoughts are with the family of the man who died."
The spokesperson added that the accident would not delay the project, as it was ahead of schedule.
The man who died has been named as Patrick O'Sullivan. He was pronounced dead at the scene after a tower crane feeding a concrete pour collapsed.
A second man was taken to Central Middlesex Hospital where he has had an operation on his leg. It is understood that both men were members of the T&G union.
T&G national secretary for construction Bob Blackman said he was deeply saddened by the news. He said: "The T&G will co-operate fully with the HSE investigation into the causes of the accident."
The probe comes after Building revealed last week that HSE inspectors are threatening to strike over pay. The union that represents the inspectors, Prospect, had given the HSE until last Friday to accept a minimum pay increase of 2.6%, but it is understood that the HSE has rejected the to demand. The union is expected to push ahead with its disputes procedure.