The six were taken to a south-east London police station, the force spokesman said.
A 29-year-old man was arrested in the street in west London, a 21-year-old man and the women were arrested at a separate residential premises in west London, and three other men, aged 18, 24, and 26, were arrested in east London.
Searches under the Terrorism Act 2000 are being carried out at eight residential premises in east, west and north London and one business premises in east London.
Public safety remains our overriding concern.
More top news
Tube and rail passengers planning to travel over Easter could be hit by major engineering projects.
Lorna McIlwaine was treating a patient who had suffered an unprovoked attack when she felt a splash of fluid fall onto her.
Despite seven deaths and 71 serious injuries in London since 2010, the LFB says manufacturers are "dragging their heels" on improvements.