Two boys, aged 2 and 3, died of smoke inhalation in the January 13th blaze.
A third child, a 6-month-old girl, is said to be doing well in a Pediatic Unit at a London Hospital.
Police say the girl is eating, smiling and interacting with others.
Police confirm the cause of the fire was accidental and no foul play is suspected.
The children's parents suffered no major injuries in the blaze.