Police officers had signalled for the car to stop prior to the crash, but the car "sped away out of sight", according to Scotland Yard.
Witnesses described a brave effort from emergency services to save the men inside the car - of which just the bumper can be seen from the street.
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"It was a really big bang, I thought the tree [next door] had come down," he told . He continued: "The man's screaming was loud at first, but then it got quieter." The man was given CPR on the steps of a Tesco's store opposite the flat, Khero said.
Another neighbour, retail manager Frank Shalloe, 57, said he heard a "massive, massive thud".
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The collision, which left the car wedged between the side of the building and steps leading to a basement level flat, took place shortly after 3am on Saturday morning.