Two men were arrested by police "supported by firearms officers" on a street in Ilford, east London, the Metropolitan Police said in a statement yesterday.
A 27-year-old was detained on terrorism charges while the second, 33, was arrested on drugs charges.
The third suspect, 29, was apprehended at a home in the same area of the British capital. He was also arrested on "suspicion of the preparation of terrorist acts", police said.
Searches were underway at the residential property and a business address in Ilford, the latest in a series of raid since the weekend assault.
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Eight people were killed in the attack, including a Frenchman whose body was found in the River Thames on Tuesday, and 48 people were hospitalised.
The latest arrests come on the eve of Britain's general election today, after a political campaign marred by the London attack and a suicide bombing in Manchester last month which left 22 people dead.
The Metropolitan Police said they had reviewed security ahead of the vote, putting in place a "specialist and highly flexible operation" which can be deployed as needed.
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