The other three victims whose inquests were opened included artist Khadija Saye, 24.
The artist, hailed as a "wonderful young woman" by Tottenham MP David Lammy, was due to appear on a BBC documentary about her work, which was on show in Venice as part of a collection on the theme of diaspora.
The inquest heard Miss Saye, also known as Ya-Haddy Sisi Saye, was found in a hallway on the ninth floor, 11 floors below her 20th floor home.
The inquest of her mother, Mary Ajaoi Augustus Mendy, was also opened. The body of Ms Mendy, 54, also known as Sissy Mendy, was found on the 13th floor.
Her provisional cause of death was "fire fumes, pending further investigation", Mr Sword told the inquest.
She was also identified via dental records.
In a family statement released by Scotland Yard on Monday, Ms Mendy's sister Betty Jackson said: "My beloved sister, words can never describe the pain of losing you.