The assistant commissioner also confirmed that the police had made two further arrests in connection with the attack, which the force has declared a terrorist incident.
“Based on what we know, counter terrorism policing has declared this a terrorist incident,” he said.
Police are stepping up patrols at Jewish sites across the country, where the many members of the community have gathered for prayer on Yom Kippur.
The assistant commissioner said it was "devastating" that the attack was carried out on Yom Kippur, and counter-terrorism police are deploying all resources possible.
He said “Communities across the UK would normally be marking this holy day are now grieving and worried about their safety. I want to be clear, UK policing is mobilising and it is mobilising fast.
“Police forces are stepping up patrols across the country, at synagogues and Jewish sites, and more widely to provide reassurance to all those communities who have been affected by this incident.”
The assistant commissioner said the force was “deploying all of our capabilities in response to what has happened” and would utilise resources from across its network to build a “full intelligence picture in the coming days and weeks.”
He asked the public to remain vigilant and be “alert to what is happening in your own communities.”
The prime minister is convening an emergency meeting of Cobra this afternoon.