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.
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.
Photos: 'Dangal' girls Sanya Malhotra, Fatima Sana Shaikh's dinner outing
Photos: Salman Khan, Daisy Shah spotted at the Mumbai airport
Photos: Rakhi Sawant to play Honeypreet in Ram Rahim biopic
Photos: Arvind Kejriwal asks Kamal Haasan to join politics
Photos: TV actress who played goddesses on the small screen