Speaking to the BBC after chairing a meeting of Cobra, the Prime Minister Theresa May thanked the emergency services for their professionalism and bravery.
She said the police were doing all they could to identify those responsible and bring them to justice but urged the public to continue to go about their daily lives.
The meeting of Cobra has not increased the threat level to critical, Mrs May said.
The threat level is only increased to critical if the security services believe the threat of another attack is imminent.
“The threat of terrorism that we face remains severe but by working together we will defeat them,” she added.
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