Screams from witnesses could be heard after the man – wearing a blue T-shirt and beige cap – raced across camera as BBC reporter Keith Doyle gave an update on Charlie Gard hearing on Monday.
Footage shows another man racing behind and stopping abruptly as the man in the blue T-shirt falls down as the bus passes off camera.
The man in the blue T-shirt races across the camera
BBC reporter Keith Doyle tries to see what has gone on behind him
Despite fears of a sickening collision Mr Doyle later tweeted the man was fine.
The Metropolitan Police issued a statement saying the man had only suffered minor injuries.
A Met spokesman told Mirror Online: "We were called at 15.10 to reports of a road traffic collision between a bus and a pedestrian.
One witness behind BBC reporter Keith Doyle holds his hands up to his face apparently in shock
"The man had an arm injury which is not thought to be life-changing or threatening.
"But upon further inquiry it appeared that the bus did not strike the man and that this was not a road traffic collision."
The man (not pictured) suffered an arm injury, Met police said in a statement afterwards
It is not known if the man was connected with the Charlie Gard protest which was taking place in the Strand at the time.
Charlie Gard's parents – Chris and Connie Yates – have been given two days to submit new evidence to try and convince a High Court judge that experimental drug treatment in the US could improve the baby's health.