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The Metropolitan Police had confirmed the incident, which injured 11 people, as a "road traffic collision" and not terrorist related soon after it created panic in the busy tourist spot in the British capital.
"Because of where this collision occurred and the number of pedestrians involved, I fully appreciate the concern and alarm this incident caused.
Enquiries have established that this incident is not terrorist related and I'd like to thank those who came to assist the injured. Thankfully there are no serious injuries with the majority now discharged from the hospital, said Detective Constable Darren Case from the Met Police Roads and Transport Policing Command.
He also made an appeal for eyewitness in the area who saw what happened, or who have any pictures or moving footage that could help police gain a greater understanding of what happened.
Eleven people were found at the scene with varying but non-life threatening injuries and nine of them were taken to hospital for treatment.
This included the driver of the car involved, who was arrested at the scene on suspicion of dangerous driving.
British Prime Minister Theresa May tweetedher thanks to first responders and members of the public, adding: "My thoughts are with the injured."
London Mayor Sadiq Khan also tweeted soon after the incident yesterday: "For Londoners and visitors planning to visit our excellent museums and attractions in the area, please be assured they will be open as usual tomorrow [Sunday]."
Besides the Natural History Museum, the Exhibition Road area is also home to the Science Museum and the Victoria and Albert Museum.
The current terror threat in the UK is at "severe" - the second highest level - meaning an attack is highly likely.
The incident caused concern due to a recent string of terror attacks involving car collisions by Islamic State (ISIS) linked terrorists across Europe.