The third London Bridge attacker has been named as 22-year-old Youssef Zaghba, a Moroccan-Italian man.
Pakistan-born Khuram Butt, 27, and Rachid Redouane, 30, both from Barking were the other two attackers.
Meanwhile, another victim has been named as Australian nurse Kirsty Boden, 28, who her family said had run towards London Bridge to help people.
Seven people were killed and 48 injured in Saturday night’s attack – the three attackers were shot dead by police.
Zaghba, Butt and Redouane drove a hired van into pedestrians on London Bridge at 21:58 BST before stabbing people in the area around Borough Market.
Armed officers killed all three within eight minutes of receiving a 999 call.
The Metropolitan Police said Butt had been subject to an investigation in 2015, but there had been no suggestion this attack was being planned.
In other developments:
- Theresa May says she expects a review will be launched by the police and security services following the attack, amid an election row over police numbers
- The Metropolitan Police said a 27-year-old man had been arrested in Barking on Tuesday in connection with the investigation
- A property in Ilford, east London, was also searched by police at about 01:30 BST, but no arrests had been made, the Met said
- The Prince of Wales and Duchess of Cornwall visited injured members of the public at the Royal London Hospital
- NHS England said 32 people remained in hospital, with 15 in a critical condition
- A national one-minute silence was held in the UK in memory of those who were killed
- All 12 people arrested on Sunday after the attack have now been released without charge
The so-called Islamic State (IS) group has said its “fighters” carried out the attack.
An Italian police source has confirmed to the BBC that Zaghba, who lived in east London, had been placed on a watch list, which is shared with many countries including the UK.
In March 2016, Italian officers stopped Zaghba at Bologna airport and found IS-related materials on his mobile phone. He was then stopped from continuing his journey to Istanbul.