"This is a very unusual incident. It is a freak accident."
Mr Squires said a man sitting on the top deck was left with a suspected broken nose while another passenger was taken to hospital with injuries to the side of their head.
Three others were treated at the scene and discharged.
London School of Economics student Ethan Meade, who posted pictures of the scene on Twitter, said he turned around after hearing a crash.
"I saw the roof fall down off the side of the bus, and the glass shatter everywhere. The passengers seemed to be sitting there pretty stunned as you'd expect," he said.
Transport for London said there would be a full investigation into the crash.
- AAP