"And it was busy, people were having to struggle to get out of there", the witness said. "It was quite scary".
A spokesman later said the incident was not being treated as terrorism-related at this stage.
Police cordons were set up outside the station and Ms Witherspoon saw one woman with a bandaged leg in a wheelchair, being attended to by ambulance staff.
A witness said that a number of people were taken away in ambulance, however the extent of their injuries is unclear.
London Mayor Sadiq Khan tweeted that he was in close contact with Assistant Metropolitan Police Commissioner Mark Rowley, who plays a lead role in the police's counter-terrorism operation. A police forensics officer in blue coveralls took pictures of the crash site.
Her colleague at Brown and Rosie, Kayla Spark, 23, said: "They came into the shop really aggressively".More news: Prosecutors reveal thwarted plot to bomb Times Square, New York subway
"There's a lot of people milling about not knowing what's going on", she said.
British officials, however, have not classified the incident as a terrorist act.
After the incident, witnesses reported a vehicle hitting pedestrians. There was no immediate statement on the number or severity of the injuries.
The museum confirmed the incident on Twitter and said it is working with the police. Full armed police locked the whole area out outside of @V_and_A in London.
The police, in a statement, said: "Enquiries to establish the circumstances and motive are underway".
Meanwhile, government sources said Prime Minister Theresa May receives regular updates regarding the incident.