"These arrests and searches are part of an ongoing investigation into Islamist related terrorism," the statement said. "A number of residential addresses and vehicles are being searched by specialist officers in west and central London as part of the investigation."
A European security source familiar with the case said investigators believe they may have foiled a plot to attack targets in Britain which was in the early stages of planning.
The source said that at least one of the arrested men is believed by British authorities to have spent time in Syria.
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Both the counter-terrorism command of Scotland Yard and MI5, Britain's counter-intelligence agency, were involved in the investigation, the security source said.
British police arrested 11 people last month in other Islamist-related operations. It was not immediately clear if the various investigations were connected.
In August, Britain raised its international threat level to the second-highest classification of "severe", meaning an attack was considered highly likely. British Prime Minister David Cameron has said Islamic State militants battling for territory in Syria and Iraq also posed a grave security risk to Britain.
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