The Metropolitan Police force said it was believed to be a traffic collision and not terrorism. "Not thought to be terrorist related", police said in a statement.
London Police say the incident is believed to be a auto crash but that there are a "number of people injured".
They added: "We are aware of injuries but await further confirmation".
A cab jumped a curb and slammed into a London shopping center Wednesday, sending shoppers running and pinning at least one person, according to reports.
The London Ambulance Service has crews at the scene, but have yet to release details of any casualties.
Photos have appeared on social media of the black cab on the pavement after it hit a number of pedestrians. Famed vlogger, Pro Syndicate, tweeted, "We just walked outside the theatre and a taxi just drove into a crowd of people walking past".
Police are still at the scene but are not treating the incident as a terrorist attack.
Four people were injured in the incident, with three taken to hospital and a fourth treated at the scene, paramedics said.