Metropolitan Police chief Cressida Dick revealed the force had launched a major probe into Saturday's cowardly ISIS attack.
She said finding out "whether anybody else was involved" in planning the atrocity, which left seven dead, was a "very high priority".
Ms Dick added: "We've been moving very, very fast. We believe we know the identities of these people who carried out this appalling attack.
We've made a number of arrests in the last 36 hours
"We've made a number of arrests in the last 36 hours, at the moment we still have 12 people in custody.
"We've carried out searches in a variety of places in east London and we've seized a huge amount of forensic material.
"So we're moving very quickly and we're working with the intelligence agencies in that work."
The Met Police has launched a major probe into the London terror attack London Bridge terror: Scenes as armed police respond Sun, June 4, 2017
At least two people have died after being after reportedly being struck by a van on London Bridge on Saturday night.
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Armed police responding to the incident at London Bridge
Ms Dick said: "We are frequently able to disrupt or indeed provide highly effective protection when we think an event or a particular place is at risk.
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"But I understand people will be concerned and all I can say is we will be doing everything in our power and we will be stepping up a gear."
Cressida Dick spoke about the possibility of a wider ISIS terror cell
Appearing on BBC radio moments later, the police chief said it was "certainly a possibility" that the attacks were triggering the next one.
She said: "The rhetoric that has been coming from Daesh and other organisations has been to encourage people to take action into their own hands, to use low-tech methods.
"And undoubtedly when people see something which appears from their perverted point of view to be successful, some people will be inspired by that."
Seven innocent people were killed in the atrocity on Saturday night
Ms Dick also said the resources available to the police needed to be looked at.
She said: "The threat seems to be changing so we need to look at our strategy, we need to look at our resourcing, we need to look at the techniques we're using.
"We've always been able to sort-of step up our game and that I'm afraid is what we clearly need to do now, as do people in our communities."