The incident happened when the car carrying Corbyn was mobbed by journalists, asking questions about Labour party's leaked manifesto.
In the commotion, BBC camera operator Giles Wooltorton's left foot was run over by the front left wheel of the Metropolitan Police vehicle carrying Corbyn.
Wooltorton was taken away by ambulance with a swollen and bruised foot but is said to be in "good spirits".
"Officers from the Met's royalty and specialist protection unit were carrying out operational work in Savoy Place when it is believed a member of public was injured by one of the vehicles," a Met Police spokesperson said.
The BBC said it was focusing on making sure its cameraman was fine.
In a statement the broadcaster said: "An experienced BBC cameraman has been injured while filming at the Labour Party manifesto meeting. He has been taken to hospital for assessment and treatment. At the moment the BBC are focusing on their duty of care, making sure that he is OK.
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