The arrests in Barking followed a raid at a flat belonging to one of the three attackers.
A van had ran over pedestrians on London Bridge on Saturday before three men got out and stabbed people in nearby Borough Market.
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The attackers were shot dead by eight officers who fired 50 bullets, accidentally killing a member of the public.
Of the 12 people who were arrested, seven are women. A 55-year-old man was later released without charge.
Meanwhile, Islamic State of Iraq and Syria (ISIS) on Sunday issued a claim of responsibility for the attack.
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In a statement more than 24 hours after the attack, the group’s Aamaq news agency quoted a “security source,” saying, “A Unit of Islamic State Fighters carried out London attacks yesterday.”