CCTV shows the three men attacking a bystander in the Borough Market before charging at armed police officers.
The police then shot the men dead.
The footage emerged as police made further arrests in the wake of the attack which claimed 8 victims.
17 people have been arrested with 5 remain in custody.
Counter-terrorism officers arrested two men in a street and another man in a separate raid on a house in Ilford, east London, late on Wednesday night, Scotland Yard said.
The first man, 27, was detained on suspicion of the preparation of terrorist acts, while the second, 33, was arrested on suspicion of possession with intent to supply controlled drugs.
The third man, 29, was also arrested on suspicion of the preparation of terrorist acts and all three have been taken for questioning while detectives search the residential address and a business premises.
Ilford, which is near Barking, has become the focus of the inquiry after it emerged that terrorists Khuram Butt and Youssef Zaghba had links to the area and there have been a series of raids in the wake of the attack.
Following the latest operation, residents in Wingate Road, south Ilford, described how armed police flooded the quiet residential street at around 10.20pm on Wednesday.
They saw a man dragged from a house and arrested while armed officers led three women out to a neighbouring garden and told them to keep their heads down.
One neighbour, who asked not to be named, said: “I looked out and saw just loads of armed police officers balaclava’d up. There were about 10 of them and loads of unmarked cars arriving.”
The neighbour said the road was cordoned off and went into “lockdown”.
He added: “There was a male arrested, but I don’t know who that was.
“I do believe from hearing other neighbours he was quite rough handled in his arrest, and dragged across the road.
“All I saw was him getting put into an unmarked vehicle.”
The neighbour said he believed a “South Asian Muslim” family live at the address.
Forensics officers were seen carrying boxes into the property in Wingate Road, which is a street away from the Ummah Fitness Centre, where the Times said the three London Bridge terrorists were filmed outside five days before the attack.
Butt, one of the men who carried out Saturday’s atrocity, worked out at the gym in St Luke’s Avenue, which was raided overnight and eyewitnesses reported that computer equipment had been taken away.
The road was cordoned off as plain-clothes officers were seen going in and out of the building, which is in a small parade of shops, as others searched underneath cars.
The latest arrests follow the detention of a 30-year-old man as detectives raided an address in Ilford in the early hours of Wednesday.
As the fallout from the atrocity continued, all eight people killed in the massacre were identified, while a further 10 victims remain in a critical condition.