Khuram Butt, a British citizen born in Pakistan, and Rachid Redouane were on Monday named by Scotland Yard as two of the three men who killed seven people during a weekend terror attack in London.
Butt, 27, was married with children and lived in Barking, east London for a number of years.
Police said Butt was known to security services but there had been no evidence of "attack planning".
Redouane,30, who also lived in Barking, claimed to be Moroccan-Libyan.
The pair and one other man were shot dead by police after killing seven people and injuring 48.
They drove their hired van into pedestrians on London Bridge before stabbing people in the area around Borough Market.
Assistant Commander Mark Rowley said: "Inquiries are ongoing to confirm the identity of their accomplice."
Butt was the supposed ringleader of the London Bridge terror attack who was photographed on the ground wearing an Arsenal football shirt with canisters strapped to his body.
Butt previously appeared in the Channel 4 documentary, The Jihadis Next Door, which warned of the rise of extreme Islam in London, The Telegraph reported.
Butt had been reported to the anti-terror police on at least two occasions, it claimed.
Rachid is believed to be the attacker who was carrying an ID card issued in Ireland when he was shot dead. There are unconfirmed reports that he may have claimed to be from Morocco and that he was married to an Irish woman and had lived in Dublin, the paper said.
Police have not identified the third attacker.
Police on Sunday arrested 12 people, among them seven women -- all of them in Barking and other parts of east London. Those arrested were aged from 19 to 60.
Counter terrorism police made two fresh raids on Monday on addresses in east London in connection with Saturday's deadly terror attack in London.
Prime Minister Theresa May earlier said the three terrorists responsible for the London attack have been identified and their names would be revealed soon.
Police said there would be "increased physical measures on London's bridges to keep the public safe".
Security had become a battleground issue ahead of Thursday's general election following the Manchester bombing last month, in which 22 people were killed as they left an Ariana Grande concert.
Pressure on May intensified when she faced a volley of questions over police cuts from journalists at a campaign event.
May defended her government's stance on the issue, saying that her Conservative government had protected police budgets.
Jeremy Corbyn, leader of the main opposition party, called on May to resign over the issue, saying earlier that "you cannot protect the public on the cheap," and promising to recruit another 10,000 police officers if he is elected into power.