The Enquirer revealed earlier this week that four workers from the site have died in their sleep at home this year.
The deaths have caused concern among the workforce who have previously flagged fears over dust levels on the job.
Two of the deaths were in the last week and another in June. The fourth death earlier this year is understood to be cancer-related.
A spokesperson for main contractor Costain Skanska Joint Venture said: “Our condolences go out to the friends, families and colleagues of those who have recently passed away.
“The safety of all colleagues working at CSJV sites is absolutely paramount.
“Independent air quality monitoring at Bond Street is conducted at regular intervals as well as for specific planned construction activities.
“This monitoring has never revealed anything concerning or unexpected.
“Any concerns raised about health and safety on site will always be fully investigated with the appropriate action always taken.”
A spokesperson for Crossrail Ltd said: “Our thoughts are with our colleagues at Bond Street and the friends and families of those who have passed away.
“Crossrail Ltd demands the highest standards of health and safety across the project and we continue to work closely with our Bond Street contractor Costain Skanska Joint Venture in support of making sure this is the case.
“Crossrail and its contractors monitor the air quality at all sites to ensure that compliance requirements are met and that workers are not exposed to unacceptable levels of dust.”
Unite regional officer Guy Langston said: “Workers at Bond Street have had genuine concerns about air quality levels for months and despite obstruction from management, Unite has ensured improvements have been made.
“The latest tragedies have again highlighted concerns with the air quality at the station and it is essential that the HSE holds a full inquiry into all elements of health and safety on the project.
“Workers should not return to work until independent testing has confirmed that it is safe to do so.”