A black taxi mounted a kerb and crashed into pedestrians in Covent Garden on Wednesday evening.
Scotland Yard said the incident is not thought to be terrorist related after a taxi ploughed into pedestrians in Southampton Street at around 5pm.
Metropolitan Police officers and paramedics from London Ambulance Service (LAS) rushed to the scene as shoppers and tourists fled from the scene in panic.
Three people were taken to hospital, including a man with a serious leg injury and a fourth person was checked over at the scene.
The driver of the taxi stopped at the scene and has been detained by police.
Market stallholders reported hearing a "big bang" after the taxi hit a phone box and people started running away.
The London Transport Authority has also added that the incident is a "serious collision".
A number of emergency vehicles were sent to the scene, including the trauma team from London's Air Ambulance who travelled to the scene by car.
Stuart Crichton, assistant director of operations at LAS, said: "We worked closely with other members of the emergency services at the scene and treated a total of four patients.
"A man was treated for a serious leg injury and taken to a major trauma centre as a priority.
"Two other patients were treated for minor injuries and also taken to hospital. A fourth patient was checked over at the scene."
The Strand was closed in both directions with traffic now backing up to Charing Cross station but has now been re-opened.
Eyewitnesses reacted with shock to the crash.
Rob Madden said: "Never seen so many police cars and helicopters in my life in London."
Alexx Pan added: "Our police really are incredible. Officers on the scene within five minutes."
Christy Gilbert said: "The police response was absolutely incredible today at Covent Garden."
People were seen running down the Strand following the incident.
There is still a heavy police presence at the scene as the area is still cordoned off by police.
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