The incident took place at Great Western Road in the early hours of this morning, Metropolitan Police said.
Help was called to the scene of the accident around 4:50 am and found the vehicle on fire.
The flames were extinguished but three people were pronounced dead at the scene.
The police are trying to identify the deceased and inform their families.
Serious Collision Unit detectives have asked witnesses or people with dashcam footage to come forward.
It is believed that no other cars were involved in the crash and several residents were evacuated from the building as a precaution.
A spokesperson for the London Fire Department said: ‘Firefighters have been called to report that a car has collided with a protected accommodation block. The vehicle was on when the teams arrived.
“The teams fought the fire and led nine people to the shelter of the block via an internal staircase.
“Three people in the vehicle were unfortunately declared dead at the scene. “
Police have set up a cordon on either side of Great Western Road.
Six officers are on hand to redirect pedestrians and traffic. The cordon at the junction of Harrow Road and Great Western Road is expected to be in place for several hours.
Anyone with information can call the police on 101 quoting CAD 917/14 Sep.