The Wolff luffing jib crane type 355 B collapsed at a housing site in Bow.
The jib crashed into nearby terraced houses killing local resident June Harvey while the tower came down on the under-construction scheme.
Four other people were injured including two Wolffkran employees – one of whom is seriously injured in hospital.
Wolffkran said: “Management and staff are deeply upset by this tragedy and express their heartfelt condolences to the family of the woman that died in the incident.
“Our thoughts are with all those affected, our own staff, and their families. We also thank the rescue teams for their work on site.
“Employees of Wolffkran Ltd have been on site since yesterday supporting the responsible authorities in their investigations and preparations to remove the crane from the site.
“The affected crane is one of Wolffkran’s most tried and tested cranes, reliable in operation worldwide, and currently in operation on 18 sites across the UK.
“The crane on the construction site in Bow was only 10 years old and was fully erected on a 22 meter tower the day before the incident.”
Police confirmed that a “multi-agency investigation” is now underway involving officers from the Met’s Central East Command Unit and Specialist Crime, the Health and Safety Executive, and the London Fire Brigade.
There have been no arrests and enquiries continue.
The crane was operating on a modular housing site for NU Living, the in-house building arm of Swan Housing Association.