Scotland Yard has named the terrorist responsible for yesterday's attack on London Bridge as 28-year-old Usman Khan.
Anti-terror police have raided a house in Staffordshire area which was linked to Khan.
Assistant Commissioner Neil Basu confirmed that a man and a woman had been killed in the attack, reports Daily Mail.
He said: "The investigation into the attack near London Bridge continues at a pace.
"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.
"However, we continue to make fast time enquiries to ensure that no other people were involved in this attack and that there is no outstanding threat to the public.
"As I stated earlier, police were called at 13:58hrs to a stabbing at premises near to London Bridge, EC1. Emergency services attended, including officers from the City of London Police and the Metropolitan Police.
"A male suspect was shot by specialist armed officers and I can confirm that he died at the scene.
"We are now in a position to confirm the identity of the suspect as 28-year-old Usman Khan (10.03.1991), who had been residing in the Staffordshire area. As a result, officers are, tonight, carrying out searches at an address in Staffordshire.
"This individual was known to authorities, having been convicted in 2012 for terrorism offences. He was released from prison in December 2018 on licence and clearly, a key line of enquiry now is to establish how he came to carry out this attack.
"Tragically, two people – a man and a woman – were killed during the attack. Three others – a man and two women – were also injured and remain in hospital.
"The circumstances, as we currently understand them, are that the attacker attended an event earlier on Friday afternoon at Fishmonger's Hall called "Learning Together". We believe that the attack began inside before he left the building and proceeded onto London Bridge, where he was detained and subsequently confronted and shot by armed officers.
"Extensive cordons are likely to remain in place for some time and I would ask the public to continue to avoid the area.
"Public safety is our top priority and we are enhancing police patrols in the City and across London."
The attacker had links to Islamist terror groups, the security source added.
The knife-wielding terrorist, who was wearing a fake suicide vest, was killed on London Bridge on Friday afternoon in full view of horrified onlookers.
The attacker was a convicted terrorist who had served time in prison and was wearing an electronic tag, according to the Times newspaper. The paper added he was attending a Cambridge University conference on prisoner rehabilitation being held at Fishmongers' Hall and "threatened to blow up" the building.
The man had two knives on his possession when he carried out the attack, which has left two people dead and a dozen more injured.
went on to quote unnamed Whitehall sources as saying the attacker had been released from prison around a year ago after serving time for a "terrorism-related offence", and had agreed to wear an electronic tag.
A maintenance worker who witnessed the London Bridge knife attack claims he was told the assailant had been in prison for terrorism offences.
Jamie Bakhit, a 24-year-old from Purley, Croydon, said he spoke to one of the men who helped wrestle the knifeman to the ground after they were taken to the Salvation Army headquarters to be interviewed by police.
He told the PA news agency: "The guy who was on top of him said he [the attacker] had been in prison for terrorism, apparently.
"Some of the guys who were on top of him were ex-prisoners and they had all been in the Fishmongers' Hall.
"The guy told me he was in prison with the attacker."
The maintenance worker said he had just turned onto London Bridge and was heading southbound when he saw the four men tackle the attacker.
Bakhit told the PA news agency: "As I got on the bridge armed police pulled in front of me. There were already four pedestrians on top of the guy on the floor. One of them [pedestrians] was shouting 'shoot him in the f***ing head'.
"I'm still in my van at this point, trying to turn around. Then the police say 'get out of the van', so I had to leave it there.
"I then saw them [police] shoot him three or four times.
"I was in shock. I wanted to get away. Everyone was shouting run because he had something across his chest. It was crazy."
Speaking before chairing a meeting of the Government's emergency committee Cobra, Prime Minister Boris Johnson said he had 'long argued' that it is a "mistake to allow serious and violent criminals to come out of prison early and it is very important that we get out of that habit and that we enforce the appropriate sentences for dangerous criminals, especially for terrorists, that I think the public will want to see."
Metropolitan Police Commissioner Cressida Dick confirmed two people died, and three others were injured in the attack.
She refused to confirm whether or not the suspect was known to police, but said: "We will be working as fast as we can to understand who this man is, where he comes from and whether there is anyone else who we need to find quickly who might be in touch with him."
NHS England confirmed one of the three injured victims was "critical but stable" while another is stable. The third victim has less serious injuries.
Johnson praised members of the public "for their immense bravery" after it emerged bystanders helped tackle the suspect to the ground and disarm him.
Johnson, called a meeting of the Government's emergency committee Cobra on Friday evening and cancelled his General Election campaigning events on Saturday. The Lib Dems have also decided to temporarily suspend campaigning.
Several people were stabbed by the knifeman before he was stopped in his tracks on London Bridge, which was the scene of the bloody massacre in summer 2017 where eight people were killed and 48 seriously injured.
Scotland Yard said the incident started at nearby Fishmongers' Hall, and that police had "bravely and professionally confronted the suspect" within five minutes of being called.
Footage on social media showed one man being urged to move away by armed officers before the suspect was shot at point-blank range, as another bystander - understood to be a plain clothes officer - could be seen carrying a large knife from the scene.
Another video appeared to show a person on a stretcher, surrounded by emergency services staff and vehicles, being given CPR by responders following the attack.
The members of the public who intervened have been widely praised, with mayor of London Sadiq Khan hailing their "breathtaking heroism".
Witnesses said the suspect appeared to be wearing a suicide vest but Neil Basu, the head of UK counter-terrorism policing, said the vest was a fake.
He said police were called at around 2pm on Friday to a stabbing "at a premises near London Bridge".
After being shot, the suspect in Friday's attack raised his arms towards his head before lying still. A second knife could be seen on the ground near his body.
Basu told reporters: "A male suspect was shot by specialist armed officers from City of London police and I can confirm that this suspect died at the scene."
The London Ambulance Service declared it a major incident and one picture on social media appeared to show a body covered with a blanket.
The Independent Office for Police Conduct watchdog said it has launched an investigation into the police shooting of the London Bridge attacker which is standard for such incidents.