Officers were called to reports of three buses and three cars in collision on the southbound carriageway near the junction with Ebury Bridge Road at approx 1300hrs on Sunday.
The Met says it appears “the driver of a Routemaster bus collided with a line of stationary traffic from the rear”.
Officers are still working to establish the exact circumstances of the incident.
The driver of the bus and two occupants of a Citroen car were taken to a central London hospital but the Met says none of their injuries are believed to be life threatening.
The Met’s Traffic Unit are asking anyone who witnessed the collision, or the events leading up to it, to contact their appeal line on 0208 285 1574.
There have been no arrests.
Mike Weston, Operations Director for London Buses, said: “At around 13:00 on Sunday 22 September three buses, a route 11, 360 and 452, and two cars were involved in a road traffic collision on Chelsea Bridge Road, SW1.
“We can confirm one of these buses was a New Bus for London vehicle.
“Our first concern is, of course, for the driver, passengers and others involved in this incident and can confirm the emergency services were in attendance. There will be a thorough investigation into this incident as a matter of urgency.”
Although Sunday’s incident is now being investigated, Mayor Boris Johnson has previously said Transport for London does not routinely investigate all accidents involving its buses.
Since 2008/09, there have been 2026 deaths and serious injuries arising from such incidents.
London Assembly Member Darren Johnson is calling on the Mayor to change the system so that TfL investigates each incident, allowing it “to learn lessons and reduce, or eliminate, the chance of a re-occurrence.”
Assembly Member Johnson commented: “The Mayor needs to commission a pattern analysis of all the collisions involving an injury, so that he can identify any hotspots, or dangerous routes, and deal with them.”
