Police said the operation was not linked to the Olympics, which start in London on July 27, but was part of a planned intelligence-led operation.
A security source said the London arrests were related to international Islamist militancy and were made at an early stage of plotting. It was not clear if any targets were identified.
During the raids, a 29-year-old man was arrested on a street in west London while the others, aged between 18 and 30, were detained at residential addresses in east and west London.
A 24-year-old man was tasered by police with a stun gun during the operation by armed officers but did not require hospital treatment.
Police said the six were arrested on suspicion of the "commission, preparation or instigation of acts of terrorism".
Detectives were searching eight homes in east, west and north London, and one business address in east London.
In a separate and apparently unrelated incident, armed police closed both carriageways of a motorway near Britain's second biggest city, Birmingham, after reports of a man acting suspiciously on a coach heading for London.
British security forces are on high alert for any signs of trouble ahead of the Olympics. Seven years ago this week suicide bombers killed 52 people in a string of coordinated attacks in London.
The motorway incident proved to be a false alarm. Police said they did not consider it to be a counter-terrorism situation and they were not treating anyone as suspect.
(Reporting by Tim Castle and Phil Noble, Additional reporting by Alessandra Prentice; Editing by Alison Williams)
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