Police said 11 people had been detained in a series of raids following the attack, in which seven people were killed and 48 others injured.
British Prime Minister Theresa May said police had identified all three attackers and would release their names "when the investigation permits."
May faced a barrage of questions Monday on deep cuts made to police numbers in the UK while she was Home Secretary. Authorities also faced scrutiny over what they knew about the alleged perpetrators of the attack in which the three men rammed a van into pedestrians on London Bridge and went on a stabbing spree in nearby Borough Market.
The three men in Saturday's assault were shot dead by police, who said the men were wearing suicide belts that turned out to be fakes.
The carnage is the third such terror attack on British soil in three months and the second in London involving the use of vehicles as weapons. In March, 52-year-old British national Khalid Masood rammed a vehicle into a crowd on Westminster Bridge and stabbed a police officer, in an attack that left five people dead.
Police said there would be "increased physical measures on London's bridges to keep the public safe," and on Monday, concrete barricades had been erected to separate pedestrians from vehicles on some of the city's major bridges.
Security had already 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 Monday when she faced a volley of questions over police cuts from journalists at a campaign event. May insisted that her record was sound, saying that she had introduced a raft of anti-terror legislation as Home Secretary. She also said that funding for counter-terrorism efforts had been protected.
Metropolitan Police Commissioner Cressida Dick said Monday that the country needed to rethink police resourcing and strategy.
But May defended her government's stance on the issue, saying that her Conservative government had protected police budgets.
"The commissioner of the Metropolitan police has said the Met is well resourced, and they are, and that they have very powerful counter-terrorism capabilities, and they do. We have protected counter-terrorism policing budgets, we have also provided funding for the increase of the number of armed police officers," she said at a campaign event.
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.
One of the victims in Saturday's attack was identified as Chrissy Archibald, a Canadian who had moved to Europe to be with her fiance.
Another 36 men and women are currently in hospital, 18 of whom are in a critical condition, according to NHS England.
A memorial is planned for 6 p.m. (1 p.m. ET) local time Monday in the capital's Potters Field Park, as the city continues to digest its second attack in two months.
London Mayor Sadiq Khan said Monday that the actions of the attackers were perverse and poisonous, adding that they had no place in Islam.
"The acts of these three men on Saturday night was cowardly, was evil and I'm angry and furious that these three men are using to justify their actions the faith that I belong to," he said.
ISIS claimed responsibility for the attack on Sunday night, although they provided no evidence for their involvement or details of the attack.
Police said they had seized a huge amount of forensic material in two early morning raids in east London Monday, as part of their efforts to determine if the three men who carried out Saturday's attack were part of a wider network.
Details of the investigation had been kept closely under wraps, in stark contrast to last month's Manchester bombing, when photos and information from the investigation were repeatedly leaked to the US media, triggering a row between the British and American governments.
Monday's early morning raids follow raids on a housing complex in Barking east London on Sunday, where a series of arrests were made.
CNN's Melissa Bell spoke to residents there who recognized a familiar face among the three dead attackers, identifying him as one of their neighbors and describing him as a family man who kept to himself.
Barking resident Erica Gasperri said she went to the police after she saw a man, believed to be the attacker, teaching the local children about Islam.
"All of a sudden we saw this individual speaking to the kids ... showing them how to pray. He was standing over there, I could see them from my window," Gasperri said.
Ikenna Chigbo, in an interview with Britain's Independent Television News, described another of the arrested men as a nice guy who regularly invited neighbors to barbecues and played football and table tennis with them.
"Yesterday -- I'm actually in the process of moving home at the moment -- I hired a van moving some bits. He came to me. He was a little bit overnice," Chigbo told the station.
"He said to me, 'Where can I get a van like that?' Asking me all the details like how much was it, where he could get a van -- basically because, he said to me, 'I might be moving shortly with my family as well.'"