Transport for London's figures show, one person a day has been killed or seriously injured in incidents involving London buses in the past five years
They were released to Greater London Authority Conservatives in response to a Freedom of Information request.
TfL's figures show, from 2008 to 2013, 1,889 people have been seriously injured or killed.
In contrast, statistics from the safer Oxford Street Blog show 2026 pedestrians and cyclists killed of seriously injured involving buses since Boris Joynson became Mayor.
Richard Tracey, Greater London Authority Conservative transport spokesman and London Assembly Member for Wandsworth and Merton said: "These figures are alarming and they remain stubbornly high.TfL said only 6% of accidents involving buses resulted in injury. The number was "actually very small and falling", TfL's head of surface transport said.
"Transport bosses need to urgently become more transparent around safety figures.
"Despite persistent questioning for several months, they have not yet been able to provide borough-by-borough breakdowns for recent serious incidents involving their own buses."
The figure of 1,889 people seriously injured or killed in five years translates as 378 a year or 1.03 a day. It is not broken down into how many died and how many were hurt.
In a report, Mr Tracey calls for TfL to publish statistics on the number of fatal and major incidents involving buses on a quarterly basis and for the worst-performing bus companies to be identified.
He also wants accident hotspots to be identified.
Leon Daniels, head of surface transport at TfL, said from next year statistics would be published by borough and route.
He said: "Although bus trips account for over 25% of road journeys in London, only 6% of road collisions resulting in an injury involve London buses, and this is falling.
"Collisions with pedestrians have fallen by around 40% since 2008/09 and fatal collisions have been reduced by around 60%."
But one victim, Tom Kearney, who was seriously injured by a bus in Oxford Street in December 2009, said TfL had a "systemic problem" and was "in denial".
Darren Johnson, Green Party London Assembly Member, said: "The scale of cycling and pedestrian casualties from bus collisions has been a neglected problem for too long.
"London relies on its buses and there are simple and easy steps that Transport for London could take to make them safer, starting by writing safety requirements into the bus company contracts."
Just a few decades ago, it wold take months of intensive training, culminating in the skidpad test, before a bus driver became qualified. Nowdays, it only takes a couple of weeks and the Skid pan has been made redundant.
TfL...Totally Failing London.
Part sourced: BBC News.