The Metropolitan Police said officers entered properties in Newham and Barking at 4.15am on Monday and "a number" of people had been detained.
Searches were continuing at both addresses, police added.
Residents reported hearing "loud flash bangs and gunshots" in the early hours of Monday morning.
Twitter user BatemanLDN said: "It woke me up along with the whole street. Extremely loud bangs followed by gunshot bangs.
"All ok - very shaken residents nearby though. All quietened down now."
Simon Tucker wrote: "Heard this in the Dagenham area at around 4:15 am. Started with loud explosion sound. Followed by about 20 shots, Some sounded distant."
Terrorists brought carnage to the streets of Britain for the second time in as many weeks, killing seven and leaving 21 fighting for their lives.
Pedestrians were mowed down by a van on London Bridge before attackers stabbed a police officer and revellers around Borough Market with 12-inch knives.
One of the attackers shouted "this is for Allah" as he knifed a man near a pub - while the Islamic State militant group claimed its fighters carried out the attack.
The group is said to have urged extremists to run over civilians in a poster released over the weekend featuring a knife, handgun and lorry urging radicals to "gain benefit from Ramadan".
The three men, wearing fake suicide bomb vests, were shot dead by eight officers outside a pub after police opened fire with an "unprecedented" hail of 50 bullets, while a bystander was also shot.
Officers say they know the identities of the men who carried out the attack and will release the names "as soon as operationally possible".
Scotland Yard said seven women and five men aged between 19 and 60 were arrested under the Terrorism Act in Barking on Sunday. A 55-year-old man was later released without charge.
A vigil will be held on Monday evening near London Bridge in honour of the victims of the attack, which took place at around 10pm, while a minute's silence will take place at 11am on Tuesday.
The first victim of the attack has been named as Canadian national Christine Archibald, who worked in a homeless shelter until she moved to Europe to be with her fiance.
Her family said in a statement: "We grieve the loss of our beautiful, loving daughter and sister. She had room in her heart for everyone and believed strongly that every person was to be valued and respected.
"She would have had no understanding of the callous cruelty that caused her death."
Network Rail said London Bridge rail and London Underground stations reopened at 5am but the rail station will be exit only.
People from around the world were caught up as hundreds cowered in pubs and restaurants, barricading themselves inside as the attackers stalked the streets.
Tales of heroism emerged in the aftermath, with one British Transport Police officer taking on the trio armed only with his baton before being stabbed in the head, face and leg.
An off-duty Metropolitan Police officer was also injured after he tackled the men.
Forty-eight people were left in hospital, 21 critically injured.
As counter-terrorism police units and security services launched a huge investigation for the third time in a matter of weeks, officers arrested a dozen people in raids on flats in Barking, east London, where residents said they believed one of the terrorists may have lived.
One neighbour said one of the attackers had recently asked him how he could hire a van.
A friend of one of the attackers also told the BBC Asian Network he had reported him to the anti-terror hotline after he began expressing increasingly radical views and justifying terror attacks, but the man said he was never arrested.
Two suspects were also detained in East Ham.
Witnesses to Saturday's attack said the terrorists deliberately drove into pedestrians on London Bridge shortly after 10pm - in the same way as Westminster Bridge attacker Khalid Masood.
Attacking people after abandoning the van, they headed to Borough Market where the pubs and restaurants were packed with Saturday night crowds, many watching the Champions League final between Juventus and Real Madrid in Cardiff.
One woman, Elizabeth O'Neill, said her son Daniel was approached by one of the men who said, 'this is for my family, this is for Islam', before sticking a knife in him.
The 23-year-old was left with a seven-inch wound from his stomach to his back and was saved by a friend who applied a tourniquet and took him downstairs in a pub.
With her son being treated in King's College Hospital, Mrs O'Neill condemned the terrorists as "callous and barbaric", saying: "These people say they are doing it in the name of God, which is an absolute joke."
Giving an update on the investigation outside New Scotland Yard, the Met's assistant commissioner Mark Rowley said "significant progress" had been made in identifying the attackers.
He said that as well as more armed police across the capital in coming days, "the public will also see increased physical measures in order to keep public safe on London's bridges".
The Government's emergency Cobra committee gathered on Sunday afternoon, for the second time that day, to discuss the attack.
Prime Minister Theresa May delivered a stark assessment of the threat facing the UK, saying that although there was no direct link between the three incidents, "terrorism breeds terrorism".
She warned Britain is in the grip of a spate of copycat terror plots and stated her determination to stamp out "safe spaces" that exist in the real world, saying: "There is - to be frank - far too much tolerance of extremism in our country."
Mrs May set out a four-pronged strategy to tackle terror by countering radical ideology; clamping down on online extremism; preventing the growth of segregated communities; and giving extra powers to police, security agencies and courts.
But Labour complained she was getting involved in political debate on a day when the parties had agreed to halt election campaigning until the evening - before leader Jeremy Corbyn denounced her record on dealing with the terror threat, accusing her of denying resources to the police and security services.
After Mrs May delivered her bleak appraisal of the risk facing the UK, US president Donald Trump, in a series of early morning tweets, lashed out at London mayor Sadiq Khan for his response to the attack, saying it is time to "stop being politically correct" about terrorism.
However, the president's criticism of Mr Khan for suggesting Londoners should not be "alarmed" was based on a clear misinterpretation of some of the mayor's comments.
In a withering riposte, a spokesman for the mayor said: "He has more important things to do than respond to Donald Trump's ill-informed tweet."
And Lew Lukens, the acting US ambassador to the UK, said: "I commend the strong leadership of the @MayorofLondon as he leads the city forward after this heinous attack."
Meanwhile, Ariana Grande returned to Manchester less than a fortnight after bomber Salma Abedi detonated a bomb in the foyer of the Manchester Arena, killing 22.
Take That, Niall Horan and Miley Cyrus kicked off the One Love Manchester benefit concert at Old Trafford to remember the those killed and the survivors of the suicide bomb attack at before Grande herself took to the stage to the delight of her thousands of fans in the audience.