The attacker, now identified by London police as paroled terror criminal Usman Khan, 28, died on the spot, officials said.
He said: "I am devastated to learn that yesterday's hateful attack on London Bridge may have been targeted at staff, students and alumni attending an event organised by the University of Cambridge's Institute of Criminology".
Three people - a man and two women - were also injured in the rampage and are being treated in hospital, Mr Basu said. Policer were carrying searches in Staffordshire in connection to the attack.
Police said Khan was convicted in 2012 of terrorism offenses and released in December 2018 "on license", which means he had to meet certain conditions or face recall to prison.
London stabbing: Armed police officers on the north side of London Bridge in London, Friday, Nov. 29, 2019.
The Times newspaper reported that Khan was attending a conference on prisoner rehabilitation organised by University of Cambridge-associated Learning Together at Fishmongers' Hall and "threatened to blow up" the building.
The attacker's history will raise hard questions for Britain's government and security services.
"Whilst we are still in the early stages of the investigation, at this time we are not actively seeking anyone else in relation to the attack", Basu said, noting that the terrorism investigation continues and police are making sure "that no other people were involved in this attack and that there is no outstanding threat to the public".
Prime Minister Boris Johnson said he had "long argued" that it was a "mistake to allow serious and violent criminals to come out of prison early".
"It is very important that we get out of that habit and that we enforce the appropriate sentences for risky criminals, especially for terrorists, that I think the public will want to see", he said.
Johnson, who chaired a meeting of the government's COBRA emergency committee late Friday, said more police would be patrolling the streets in the coming days "for reassurance purposes".
The violence erupted less than two weeks before Britain holds a national election.
The officers confronted the suspect - who was wearing what is believed to be a hoax explosive device - within five minutes of receiving the initial call.
Simon McMullan told The Telegraph: "It has been very bad to watch events unfold at London Bridge two years on from the attack which took our son James".
Learning Together is a group set up in 2014 by Cambridge University lecturers Ruth Armstrong and Amy Ludlow, with the goal of promoting social justice by "bringing together people in criminal justice and higher education institutions".
The bystanders were scene tackling the suspect before police shot him dead.
Videos on social media appeared to show passers-by holding down the suspect on London Bridge.
One of the cops then pulls the civilian off the terrorist, the video shows.
One man dressed in a suit "ran through traffic" to seize the massive blade from the terrorist before walking away from the scene and ushering innocent pedestrians away.
Karen Bosch, who was on a bus crossing the bridge, said she saw police "wrestling with one tall, bearded man" and then heard "gunshots, two loud pops".
Police on Cannon Street in London near the scene of an incident on London Bridge in central London following a police incident, Friday, Nov. 29, 2019.
Bystanders held the man down until police could get to him.
He explained: "I was driving, I stopped the auto and ran towards it".
"So Stevie and I just thought what to do, and just ran towards it, left the cars where they were and tried to do our best to apprehend the suspect".