Located in the multi-ethnic area of Barking, the flat where British media reported the man lived was raided by police on Sunday and an AFP photographer saw women in headscarves being taken out - their faces covered.
As the investigation continued, armed officers carried out two separate raids on Monday morning, one in Newham and another in Barking.
Police and the M15 domestic security agency also acknowledged Monday that they had been aware of one of the three alleged London Bridge attackers, Khuram Shazad Butt, 27, a British citizen born in Pakistan, but they had no specific intelligence to indicate he was plotting a terrorist assault.
One of Butt's neighbours, Ikenna Chigbo, told Reuters he had chatted with Butt - known locally as "Abz" - just hours before the attack on Saturday and said he appeared "almost euphoric".
Police asked for people with information about any of these men to come forward.
Both Butt and Redouane were shot dead by police within eight minutes of the first call, authorities said, adding they were still inquiring into the identity of the third attacker, who was also shot dead at the scene.
President Donald Trump continued a long-running feud with London's mayor on Monday, criticizing him on Twitter for the second day in a row in the wake of the deadly van and knife attack in the city.
Saturday's rampage was the latest in a string of attacks to hit Europe, including in Paris, Berlin and Saint Petersburg.
Dick said police had seized "a huge amount of forensic material" after going through the van used in the attack "very very carefully".More news: Two blasts at transport terminal in Jakarta
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He said he supported calls for her resignation for ordering cuts in police forces while she served as Britain's home secretary.
Britain's response to the terror threat must change, she said.
An off-duty police officer was also injured and remains in critical condition.
May said she thought London Mayor Sadiq Khan was doing "a great job". He said the idea was his father's, but it was embraced by the whole family.
London terror attack: If London Mayor Sadiq Khan had his way, US President Donald Trump would not be able to visit London or even the United Kingdom in the near future. As well as carrying knives, the attackers wore fake suicide vests, created to spread more fear.
British Prime Minister Theresa May on Sunday blamed "evil" Islamist ideology and vowed to crackdown on extremist content online worldwide, warning that attackers were "copying one another".
However, Corbyn said the best way to get May out is for people to go out and vote.
Another, written by the "Boro Bistro family", said in French: "Alex, I hope that the place where you are now will be even more attractive and peaceful than the desert of Jordan".