The Metropolitan Police clarified that the operation was not linked to the forthcoming Olympic Games.
The men and woman were all arrested on suspicion of the commission, preparation or instigation of acts of terrorism under the Terrorism Act 2000, and have been taken to a south east London police station where they remain in custody.
According to details released by the police, one man, 29, was arrested in the street in west London, while another man, 21, and the woman, 30, were arrested at separate residential premises in west London.
Three other men, aged, 26, 18 and 24, were arrested at a residential premises in east London.
The 24-year-old man was tasered during his arrest, but did not require hospital treatment, the police added.
Searches under the Terrorism Act 2000 were also being carried out at eight residential premises in east, west and north London and one business premises in east London.