There have been questions about his handling of events surrounding the shooting.
Blair has also been embroiled in a high-profile row with the force's most senior Asian officer, Tarique Ghaffur, the assistant commissioner, who has accused him of racial discrimination.
The Times newspaper had said that ministers and other police chiefs were secretly preparing plans to remove Blair, who has been dogged by controversy since taking over in February 2005.
Blair has regularly been criticised in the media.
Questions had also been raised over a series of IT contracts worth £3m ($5.3m) awarded to Impact Plus, a consultancy owned by his long-time friend Andy Miller.
Jacqui Smith, the interior minister, said Paul Stephenson, the deputy commissioner, will take over as acting head of the Met.