Police have named two of the London Bridge attackers, who drove a van into pedestrians and stabbed bystanders before being shot dead by police.
Their names were given as Khuram Butt and Rachid Redouane.
They said Butt, who was 27, was a Pakistan-born British national known to MI5.
Redouane, a 30-year-old who police said was claimed to be of Moroccan and Libyan descent, was not known to British Authorities however.
They said he also went by the identity Rachid Elkhdar.
Police said there was no evidence the attack had been planned.
They said inquiries into the identity of the third attacker were ongoing.
The three attackers were shot dead by police after driving into pedestrians on London Bridge and stabbing people in Borough Market.
The attack left seven people dead, as well as the attackers, and 48 injured. NHS England said 36 people remained in hospital, with 18 in a critical condition.
It comes as police have searched more addresses in east London.
Police said a "number of people" had been detained following the raids, in Newham and Barking.
Eleven people are being held after police raids in Barking on Sunday. One of the properties is believed to be the home of one of the attackers.
Security sources in Dublin have said one of the attackers was carrying an identification card issued in the Republic of Ireland when he was shot dead, the Press Association has reported.
British Prime Minister Theresa May said victims included a "number of nationalities", saying it was "an attack on the free world".
She said Britain's terror threat level would remain at "severe" after the London attacks, but additional security measures were in place, including at several bridges in central London.
Mrs May said a terrorist attack was highly likely.
The terror threat level was raised for a time after the suicide bombing attack in Manchester that killed 22 people just over two weeks ago.
Meanwhile, Met Police Commissioner Cressida Dick said a "huge amount" of forensic material and evidence had been seized from the van - as well as from the police raids.
She told BBC Breakfast the investigation was moving very quickly and the priority now was to establish if anybody else was involved in the plot.
She said London police would review every aspect of their approach to terrorism after the attack, which was the third in three months in the country.
She said she would like more resources, but did not want all police in Britain to carry guns.
The Islamic State militant group has claimed responsibility for the attack.
A message from Muslim faith leaders was read outside New Scotland Yard by Met Commander Mak Chishty urging the community to "root out the scourge of terrorism which hides amongst their own people and masquerades as Islam".
One unnamed man told BBC one of the attackers had become more extreme over the past two years.
"We spoke about a particular attack that happened and, like most radicals, he had a justification for anything - everything and anything.
"And that day I realised that I need to contact the authorities," he said.
He said no action was taken.
"I did my bit... but the authorities didn't do their bit".
London Bridge rail and Tube stations both reopened early on Monday morning. The bridge and surrounding roads have also reopened.
- BBC / Reuters