They previously identified two other men as attackers: 27-year-old Khuram Sharzad Butt, a British citizen born in Pakistan, and 30-year-old Rachid Redouane, who "claimed to be Moroccan and Libyan". Check back for updates.
The Metropolitan Police said two men, aged 34 and 37, were arrested in the neighbourhood of Newham and a third, aged 22, was detained in nearby Waltham Forest, Efe news reported.
Charisse O'Leary said she has "shed many tears for the people caught up in this horrific incident".
Shahid allegedly provided al-Qaida terror training to Mohammed Siddique Khan, one of the four suicide bombers who killed 52 people during London's morning rush hour in 2005.
The country's official terror threat level remains at "severe", one notch below the highest.
Police said Tuesday he is from east London and his family has been notified.
On Monday, June 5, 12 people arrested in Barking as part of the investigation were released without charge.
Saturday's rampage followed a suicide bombing that killed 22 adults and children at a pop concert in Manchester two weeks ago, and an attack in March when five people died after a auto was driven into pedestrians on London's Westminster Bridge.
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London police said late on Tuesday that they feared a French tourist, 45-year-old Xavier Thomas, had been thrown into the River Thames by the attackers' van and drowned.
Armed officers killed all three attackers within eight minutes of receiving an emergency call.
Butt, one of the men who carried out Saturday's atrocity, worked out at the gym in St Luke's Avenue, which was raided overnight and eyewitnesses reported that computer equipment had been taken away.
Assistant Commissioner Mark Rowley said Butt was known to the security services, but there was no evidence of "attack plan".
The extremist, who was shot dead along with two accomplices, after murdering seven and injuring dozens more in the attack, had access to tunnels under Parliament after he worked at Westminster tube station.
Zaghba visited her at her home near Bologna several times and in March 2016, after being stopped at Bologna airport, he was investigated for possible worldwide terrorist activity but released, according to the newspaper.
"A person going to Turkey with a backpack aroused some suspicion, also because he told the agent who checked him that he wanted to go and be a terrorist, then he corrected himself", Amato said.
The violence occurred on Saturday night in the Southwark area of London.
The Islamic State has since claimed responsibility for the attack.
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