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.
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The retrospective is so in-demand the museum will open its doors all through the night for the first time since it opened in 1857.