Haydon said he expected more arrests and searches as the inquiry continued against a backdrop of unprecedented attack planning and terrorist threat level.
Two unarmed police officers have been hailed as heroes for their bravery in taking on the London Bridge terrorists.
Two of the men, aged 27 and 29, were held on suspicion of preparing acts of terrorism while the third was detained over suspected drugs offenses.
"All three were arrested on suspicion of the commission, preparation or instigation of terrorism offences", the Met Police said in a statement.
Police continue to search the Ilford home and a business in Ilford as well, authorities said.
CCTV footage released on Wednesday showed the three men walking around Borough Market before rounding on one man. Police arrive and fired bullets into the three men as they lunged toward them, killing all three.
The developments came as families of the London Bridge attackers expressed their disgust at the murderous rampage which left eight people dead on Saturday.
In preparation for Thursday's general election, London police said they had put in place a "specialist and highly flexible operation" ready for deployment at a moment's notice.
"He is thought to have been skateboarding in a park when he stopped to defend a woman who had been injured in the attack near Borough Market".
The attack on parliament, which was in session at the time, lasted more than three hours.
Butt, 27, Rachid Redouane, 30, and Youssef Zaghba, 22, were all killed by police.
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He also said he apologized to Constand and her mother because he felt guilty of the large age gap between himself and his accuser. He said the effects Constand described in her testimony "could be consistent with ingestion" of Benadryl.
A volley of gunfire in unleashed during the melee and all three perpetrators are felled within seconds, the footage shows, eight minutes after the emergency services were first called.
The videos were published before the Metropolitan Police made three further arrests in connection with the attack.
Redouane, a 30-year-old who described himself as Moroccan-Libyan, did not come up on MI5's radar.
Valeria Khadija Collina said her son Youssef Zaghba, an Italian national of Moroccan descent, told her he wanted to go to Syria to start a family in a religious Islamic climate - not to fight. The incident left eight dead and more than 40 injured. The Metropolitan Police said the package was not terror-related in the end.
She said she had been separated from Redouane for six months.
Her family said in a statement: "We are deeply saddened at the tragic loss of our attractive daughter and sister of Harrison and Scott".
Youssef Zaghba is said to have been stopped by Italian officers trying to travel to Syria past year and added to an worldwide database of alerts about individuals, to which the United Kingdom has access. "And after I thought that these images of a garden were similar to the images of paradise".
The man, who has not been named, said: "I am truly moved and overwhelmed by all the support and comments that I've received, not only from people in this country but across the world".
"We're pushing the British authorities because, frankly, this isn't the kind of thing that can go on and on", Spanish Foreign Minister Alfonso Dastis told the news agency Efe earlier in the week, according to The Guardian.
London officials said a large part of the outer cordon of the crime scene had reopened.
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