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
The London property market is expected to be the hardest hit as buyers sit it out to see how the economy will be affected.
The former London mayor paid tribute to David Cameron just hours after the Prime Minister announced his resignation.
The pound crashed to its lowest level in 30 years as Britain voted to leave the EU.