McGee has named the worker killed at 20 Grosvenor Square yesterday as 33-year-old father-of-two Dainius Rupsys.
Mr Rupsys, a Lithuanian national, was killed at the residential conversion site in Mayfair on Monday 14 April when a mini-digger fell through the second floor to the first floor level at approximately 3.45pm.
In a statement, McGee chief executive Declan Sherry said a piece of machinery was demolishing a concrete floor slab of around 12 sq m, when the floor slab gave way and fell to the next level down.
A 29-year-old man, who the Metropolitan Police Service said was working in the digger at the time, was taken to hospital with minor injuries and was discharged on Monday evening.
Both Mr Rupsys and the man in the digger were believed to have been working on the second floor of the building when it partially collapsed, causing both to fall to the level below, the MPS said.
Mr Sherry said: “The deceased worker was Dainius Rupsys, a 33-year-old Lithuanian national who had worked with McGee since 2012. His next of kin have been informed.
“Dainius was a popular and valued member of the team and will be missed by us all. He was a father of two. Our thoughts are with his whole family at this very difficult time.
“McGee is in contact with members of his family and will be offering counselling and other support. We will also be offering counselling and support to other employees who work on the site.”
Work at 20 Grosvenor Square, the former US Naval Headquarters which is being converted into luxury apartments, has been suspended.
The Health and Safety Executive has launched a full investigation into the incident and McGee said it is providing its full support and co-operation.
“This is a difficult time for all involved and we extend our deepest sympathies to the families of the men involved,” Mr Sherry added.
“We would also like to thank staff at the London Ambulance Service, University College London Hospital, the Metropolitan Police, the Air Ambulance and London Fire Brigade for their swift and highly professional response to this incident.”
McGee was the contractor responsible for the residential building site in central London when the incident occurred.
The Metropolitan Police Service confirmed on Monday that a man, believed to be in his early 30s, was pronounced dead at the scene.
In a statement issued at 9pm on Monday, Mr Sherry said: “It is with deepest regret that we advise that, following a serious incident this afternoon on the 20 Grosvenor Square site, tragically one worker has suffered a fatal accident.
“Another worker suffered minor injuries and was taken to hospital but is expected to be released shortly.
“Work on site has been suspended and we are of course working closely with the investigating authorities to ensure that a full inquiry is conducted into this tragic incident.
“Our thoughts and deepest sympathies are with both families and friends at this difficult time.”
20 Grosvenor Square is the former US Naval Headquarters. It is being redeveloped to provide 27 residential apartments with underground car parking.
A spokesman for the Health and Safety Executive confirmed it was aware and investigating the incident.