June Harvey was found on the first floor of her home after the 20m (65ft) crane crashed down in Compton Close, Bow, at about 14:40 BST on Wednesday.
A construction worker still remains in a critical condition in hospital.
Ms Harvey’s family said she was a “true Eastender”, who loved gardening and bingo.
Her niece Jacqueline Atkinson, 63, who also lived in the house with her 28-year-old son Sam and their dog, was just metres away from Ms Harvey when the crane hit their home.
Ms Atkinson said: “I was upstairs in the same room as June when the crane hit.
“My son managed to help me escape by pushing a ladder up to the bedroom window and helping me climb down.
“I couldn’t believe it when I saw the crane had smashed into the house, leaving it like a pile of rubble.
“There was dust everywhere and Sam and I were both taken to hospital, but sadly June didn’t make it.”
Her son, a chef at Canary Wharf, said the noise was so loud he thought it was a “plane crash”, and told of his and his mother’s “miracle” survival.
“We need answers about how this happened. We have lost everything and now we have a funeral to arrange,” Mr Atkinson said.
Ms Atkinson said Ms Harvey, who had worked as a sewing machinist, moved into their house last year so she and her son could help look after her.
“She was loyal and caring, a true Eastender,” she said.
“She was a wonderful woman who was totally dedicated to her family. We are beyond devastated by what has happened.”
Her family have set up a GoFundMe page to help pay for her funeral, which has so far raised more than £2,000.
The crane was being used by Swan Housing Association and NU Living to build flats on the site of a former electrical sub-station building.
An investigation is under way involving the Met Police, the Health and Safety Executive and the London Fire Brigade. No arrests have been made.
A spokeswoman for Swan Housing Association and NU Living said they were “deeply saddened” by Ms Harvey’s death.