Michael Boateng and Hakeem Adelakun are the third and fourth people charged in connection with the investigation into an alleged international illegal betting syndicate.
Chann Sankaran and Krishna Sanjey Ganeshan were charged on November 28 and remain in custody.
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The operation to recover the unexploded bomb near the Houses of Parliament let to disruption in central London overnight.
Southern parts of England and Wales will see sunny skies after a frosty start.
A police spokesman said the incident in the Bourke Street Mall on Friday was not related to terrorism.