Counterterrorism police carried out a search Tuesday in East London as part of the investigation into Saturday's deadly terror attack.
Metropolitan Police said officers were conducting the search at an address in the Ilford section of city, and that nobody had been detained.
On Monday, authorities named two of the three attackers who killed seven people and wounded more than 50 others.
British citizen Khuram Shazad Butt, 27, was previously known to authorities, but had not been viewed as a serious threat.
"There was no intelligence to suggest that this attack was being planned, and the investigation had been prioritized accordingly," police said in a statement.
The second attacker was identified as 30-year-old Rachid Reouane.Both men lived in the same area of East London.
Police are continuing to investigate the identity of the third attacker.
Authorities also said Monday they had released without charge the 12 people police arrested in connection with the attack investigation since Saturday.
British Prime Minister Theresa May said police also are still working to determine the identities of all the victims, but that so far it is known they include people of several nationalities.
"This was an attack on London and the United Kingdom, but it was also an attack on the free world," she said.
London mayor Sadiq Khan thanked the police in a statement Monday for "running toward danger" and risking their lives for civilian safety.
"All of us pay tribute to the amazing work of the police and emergency service," Khan said. "The speed of their response led to fewer lives being lost."
Police have said Saturday's attack involved three men who were inside a van that struck pedestrians on London Bridge, then got out and stabbed numerous people at a nearby market area before being shot dead by police.
"We are trying to find out whether anybody was helping them and to understand the background to this attack as best as we possibly can," Metropolitan Police Commissioner Cressida Dick told Sky News.
The Islamic State group claimed responsibility for the attack through its Amaq news agency.
May said Sunday that three terrorist attacks in Britain in the last three months are "bound together by the evil ideology of Islamist extremism."
There is "far too much tolerance for extremism in our country," May said. "We need to be more robust in identifying and stamping out extremism in public service and across society...it's time to say enough is enough."
No link to Manchester attack
May said Saturday's attack does not appear to be connected to the a suicide bombing last month that killed 22 people after an Ariana Grande concert in Manchester or another attack on pedestrians on Westminster Bridge in March.
But she said "terrorism breeds terrorism" and that the perpetrators are "copying one another."
London Mayor Sadiq Khan condemned the attack saying, "There is no justification whatsoever for such barbaric acts."
Farhad Ahmad, a London Imam, told Sky News "people need to be told that there is no support for this in Islam at all."
Bahrain, Kuwait, Oman, Qatar and the United Arab Emirates each issued statements condemning the attack and expressing support for Britain.
At a Mass marking Pentecost, the end of the Easter season, Pope Francis asked for prayers for the victims and their families. He also prayed for "peace to the whole world" and for the wounds of war and terrorism to be healed.
Commander Mak Chishty of the Metropolitan Police read a statement denouncing the attack on behalf of the London Muslim community Monday.
"The Muslim community appeals to all sections within their own communities to root out the scourge of terrorism which hides amongst their own people and masquerades as Islam," he said.
A moment of silence also was held in Manchester, where American pop singer Ariana Grande returned to headline an all-star concert to raise money for the victims of the May 22 suicide bombing.
Fifty-thousand people, including some who were wounded in the concert attack, attended the show, which raised more than $2.5 million.
In Photos: London attack aftermath