The car was being pursued by police at the time of the collision, which happened at about 4:30 a.m. local time (0330 GMT) on Monday, the London-based Evening Standard newspaper reported.
Three people in the car were also injured. A male was arrested on suspicion of dangerous driving.
The car smashed into a shoe shop. "The car was in a really bad condition. I can't believe it. It was totally broken," a witness was quoted by the report as saying.
All four people were taken to hospital but their current conditions are unknown.
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