Scotland Yard said the men were arrested Sunday under the Terrorism Act 2000 on suspicion of the commission, preparation or instigation of acts of terrorism, The Daily Telegraph reported.
Armed officers were deployed because it was feared the men could have access to weapons, the Telegraph said.
Police shot out the tires of a vehicle in east London while pursuing two of the men, each age 25, the Telegraph reported, adding witnesses reported observing police ram the rear of the car, while a helicopter hovered overhead, before it was brought to a stop Sunday evening.
In simultaneous actions, a man, 28, was stopped by police as he walked down a west London street, and a fourth man, 29, was arrested in a home in southeast London, the Daily Telegraph said.
The BBC said the alleged Islamist plot was believed to have involved firearms and had been being monitored for some time.
The four men were booked at a south London police station as six homes across London and two vehicles were being searched, officials said. Their identities were not released.
In a statement, Scotland Yard said the arrests were made during a "pre-planned, intelligence-led operation. ... Public safety remains our overriding concern."
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