All three London Bridge terrorists have been identified as a security service probe into the atrocity looms and questions mount for the police and MI5.
The third attacker was named as Youssef Zaghba, an Italian national of Moroccan descent, who was living in east London.
According to the mother of the 22-year-old, he became radicalised online, echoing concerns raised by Prime Minister Theresa May that the internet can be fertile ground for breeding extremism.
"We have always been checking his friendships and verifying that he was not trusting the wrong people, but he had the internet and from there he got everything," Valeria Khadija Collina told L'Espresso in Bologna.
Zaghba was stopped at Bologna's airport trying to fly to Turkey in March last year over concerns he was intending to travel on to Syria, according to reports.
The youngest of Saturday's attackers is said to have told Italian authorities "I'm going to be a terrorist", while officers reportedly found Islamic State-related material on his mobile phone when they intercepted him.
Counter-terror agencies are already facing intense scrutiny after it was revealed another member of the terror gang, Khuram Shazad Butt, 27, had been known to security services.
In other developments:
:: There were fears for missing French national Xavier Thomas, 45, who police said could have been thrown into the River Thames after being struck by the van.
:: The Metropolitan Police said all of the 15 victims currently in critical care had been identified, as public appeals continued for several people who have not been located since the attack.
:: Detectives arrested a 27-year-old man under the Terrorism Act at an address in Barking, east London, shortly after 8am on Tuesday, while search warrants were also executed at addresses in Barking and Ilford.
:: A man in his 30s was arrested by Irish police in Wexford county, south of Dublin, and questioned over documentation connected to Redouane.
:: The arrest took the total number held as part of the investigation to 14, with 12 released without charge.
:: Claims emerged that Butt was reported to counter-terrorism authorities almost a year before the deadly attack after a "violent scuffle" with a member of an anti-extremism organisation
Zaghba was said to have been placed on a watch list by Italian authorities and flagged to their Moroccan and British counterparts, but a lack of evidence about his intentions meant his phone and passport were returned, Italian media reported.
There has been no official comment on the reports from UK authorities, but Scotland Yard said Zaghba was not a police or MI5 "subject of interest".
Butt was investigated by officers in 2015 but they found no evidence he was planning an attack and he was "prioritised in the lower echelons of our investigative work", police said.
The disclosure means perpetrators in all three of the terrorist outrages to hit Britain this year had at some point appeared on the radar of security agencies.
Theresa May said a review had been launched after the Manchester bombing last month and she expected the same process following Saturday's rampage.
The Prime Minister told Sky News: "MI5 and the police have already said they would be reviewing how they dealt with Manchester and I would expect them to do exactly the same in relation to London Bridge."
Butt, a father-of-two who appeared on Channel 4 documentary The Jihadis Next Door, was also reported to the anti-terror hotline in 2015 for showing signs of "extremism or radicalisation".
Lord Carlile, a former counter-terror laws watchdog, told the Press Association: "In my view, we need to review what happened in his case, and learn the lessons so that the methodology of the response to known suspicions is improved."
Zaghba, Pakistan-born British citizen Butt and Rachid Redouane, 30, who claimed to be Moroccan-Libyan, launched a murderous rampage around London Bridge and Borough Market on Saturday night.
Butt and Redouane, who also used the name Rachid Elkhdar, lived in Barking, while Zaghba is reported to have worked at a restaurant in London.
Seven victims were killed and dozens injured in the spree, which ended when armed police shot dead the knife-wielding extremists just eight minutes after the first emergency call.
The Islamic State terror group has claimed responsibility for the massacre, which sparked fears that Britain is in the grip of a wave of copycat incidents.
Authorities say the threat is unprecedented, with 500 active investigations involving 3,000 individuals in addition to 20,000 former subjects of interest.
Eighteen plots have been stopped since 2013, including five since the Westminster attack.
Labour leader Jeremy Corbyn expressed concern that the police and security services lacked the resources they needed to deal with the terrorist threat.
"Obviously, we're all worried that this could happen again. That does require obviously vigilance but it does require proper resources and therefore cutting police numbers and not funding sufficiently those that are involved in security is a problem," he said.