The crash, which police said was not terror-related, happened at the private Study Prep girls’ in Wimbledon on Thursday morning.
“A second eight-year-old girl was taken to hospital where she remains in a life-threatening condition,” London’s Metropolitan Police said in an update.
“A woman, in her 40s, also remains in hospital in a critical condition,” the police added.
They said “a number of other people”, including a seven-month-old girl, were also taken to hospital but their condition was not life-threatening.
“It is difficult to imagine the pain and upset the families of those involved are going through and we will do all we can to support them as our investigation continues,” Detective Chief Superintendent Clair Kelland said in the statement.
The police, ambulance and fire service were called to the scene on Camp Road, near Wimbledon Common, after the incident just before 10:00 am (0900 GMT) on Thursday.
Aerial footage of the building showed a gold-coloured Land Rover car stopped at an angle against the wall of the modern school building.
The driver of the vehicle, a 46-year-old woman from Wimbledon, was detained at the scene and taken to hospital, police said Friday.
Her condition was assessed as not life-threatening, they said.
She is suspected of causing death by dangerous driving and has been bailed pending further inquiries, according to the police.
The Study Prep school takes girls aged four to 11. It is split into several sites, with the youngest pupils taught on Camp Road, near the Royal Wimbledon Golf Club.
Thursday was the last day of term for children aged four to eight, according to the school’s website.
Everyone at the school was “profoundly shocked” by the crash, it said in a statement. “Our thoughts are with the bereaved family and with the families of those injured at this terrible time.”