The knifeman, wearing a suspected hoax explosive device, was shot dead by police after Friday's daylight assault that also saw bystanders intervene to try and disarm him.
Basu said Khan had been living in the Staffordshire region of central England and officers were searching an address in that area.
The event at Fishmonger's Hall was called"Learning Together", Basu said - part of a project run by academics at the University of Cambridge's criminology institute. A White House spokesman said President Donald Trump had been briefed on the attack and was monitoring the situation.
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