A witness claimed they saw one of the horses bolt across Buckingham Palace Road into a parked vehicle before galloping off.
Onlookers reportedly screamed and ran as the animal raced towards them, according to witnesses.
The Telegraph is reporting one witness, Bashir Aden, 48, a construction worker, as saying: “I saw a soldier falling down into the street after the horse ran into a car. One of my colleagues called the police.
“The man hit the floor hard, he was screaming in pain. You could see blood all over the parked car.
“The horses come down this route every day, but today the horse looked stressed or panicked. I saw the horse run away after it hit a bus. People were screaming and running all over.”
Mr Aden, who lives in Canary Wharf, east London, said: “The injuries looked very serious he looked really hurt.”
