British police on Tuesday named the third London Bridge attacker as an Italian national of Moroccan descent, and Italian officials said they had passed on their concerns about him to British intelligence officials past year.
Police on Tuesday also arrested a 27-year-old man in Barking on suspicion of violating the Terrorism Act and a residence there was being searched.
A van ploughed into pedestrians and several people were stabbed in central London on last Saturday, killing seven in what police called a "terrorist" attack days before a general election.
On Tuesday, London police appealed for the public's help in finding French national Xavier Thomas, 45, who has been missing since Saturday's attack.
The other two attackers were named Monday as Khuram Shazad Butt and Rachid Redouane.
In the wake of the London Bridge attack after Theresa May took the unusual step of calling publicly for a review, the British domestic intelligence agency MI5 will take a hard look at its counter-terrorism operations.
After a period living together in Morocco, Zaghba's parents separated and the mother returned to Italy, Corriere wrote.
Metropolitan Police said in a statement that Thomas was in town for the weekend with his girlfriend.
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They include a teenager who went to the same gym as Butt who said he was approached to join Islamic State, and a woman who told police she feared he was trying to radicalise children, The Times said.
"Although he didn't say anything in particular, I could feel it in his voice", she said.
Transport for London has confirmed that Butt worked as trainee customer services assistant for six months past year.
According to his mother, Zaghba planned his trip to Syria for at least a year prior to his detention in March 2016.
The search was a precaution after Butt's link to Pakistan was uncovered by British investigators.
Police said on Wednesday night that they had arrested another three men, meaning that they are now questioning five men in connection with the attack. All others who had been arrested have been released without facing charges.
One of those they were most concerned about was Butt.
Although they lived separately, he in Morocco, she in London, Redouane applied for an Irish visa in 2014 under rules covering marriage to an European Union citizen, according to the report.
As the fallout from the atrocity continued, all eight people killed in the massacre were identified, while a further 10 victims remained in a critical condition.