Warning: Contains graphic description of attack
Local MP Nick Raynsford said he had been told the man attacked in the street was a soldier serving at the Royal Artillery Barracks near the attack.
Mr Raynsford said the soldier had been returning to the barracks after a day out when he was attacked.
London Ambulance Service said one man, believed to be the victim of the machete attack, had died in the incident and two others were injured, one seriously.
Photo: @BietLe_
Several witnesses described seeing a "beheading" while another described seeing a man wearing a Help for Heroes T-shirt being attacked with a machete-style knife and dumped.
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Prime Minister David Cameron called a meeting of the Government's Cobra crisis committee, describing the incident as "truly shocking".
Cobra meetings are crisis response committees set up to coordinate the actions of different agencies, including the security services, police and local authorities.
The BBC reported sources had told them the men were shouting "Allahu Akbar" as they carried out the attack and had filmed carrying it out.
One witness, called James, told LBC radio: "We saw clearly two knives, meat cleavers, they were big kitchen knives like you would use in a butcher's, they were hacking at this poor guy, we thought they were trying to remove organs from him"
"These two guys were crazed, they were not there, they were just animals. They then dragged him from the pavement and dumped his body in the middle of the road.
"They took 20 minutes to arrive, the police – the armed response."
Photo: PA
He added: "There was only a few people at first then traffic began to build up because people were getting out of their cars to shout at them they were taking no notice, they were standing there, I think they were proud of what they were doing.
"When they dumped the body in the road, these two black guys had the opportunity to hurt other people if they wanted to because there were brave women with the dead guy on the floor, they were shielding and covering him. The attackers with the knives were standing over these women.
"The guy with the gun, the tall guy with the beanie cap on, even a bus had pulled up – he was going over to the bus and asking people to take his photo."
Luke Huseyin, 32, who lives in a block of flats on John Wilson Street, Woolwich, close to where the incident happened.
He said: "I was at home and heard a big bang. I looked out of the window and saw a car had crashed.
"It was a blue Vauxhall.
"Then two black guys got out of the car dragging a white guy across the road towards the wall.
"One of the guys had a knife that looked about a foot long and a machete and the other bloke had a gun.
"They started slashing him up with the knife and hitting him in the stomach with the machete.
"I don't think it took long before he was dead.
"There were people passing by who were screaming and running away. I've never seen anything like it.
"I'm still really shaken up.
"When he was dead, they dragged him out into the road and left him there.
The scene near John Wilson Street. Photo: PA
"It was strange, they didn't run off, they just stood there as if they were waiting for the police.
"It must've taken about 20 minutes for the police to arrive, I think it must've been because they were waiting for armed police.
"The police officers got out of the car and the two black men ran towards them with the gun.
"The police shot them.
"They fell to the ground. Then a helicopter landed.
"Think it must've been an air ambulance.
"The paramedics got out and I think they were working on the two men to try and keep them alive.
"I don't know if they died, they were taken away in the helicopter.
"A blanket was put over the white guy lying in the road.
"I just can't believe what I saw."
Eyewitness Michael Atley, 28, who works for a building maintenance firm nearby, said the two killers were in a blue BMW 3 series which mounted the pavement and knocked the victim over.
They then beheaded him with either a meat cleaver or a machete before both were shot by police officers who were on the scene within moments.
He told the Telegraph: "We heard the gunfire from the police shooting the two people. There were a few shots, then a pause, then some more shots, maybe eight shots in total.
"I spoke to an eyewitness who had seen the whole thing and he said they had run the guy over and then started decapitating him.
"When the police arrived the black guys were waving a pistol and a machete or a meat cleaver in the air and the police opened fire.
"When I got there the police were rushing to the bodies of the people they had shot.
"A helicopter landed in the middle of the road and took the victim away. There was a lot of blood. The paramedics wear blue gloves and they were covered in blood."
He said children at a nearby school were locked in by their teachers.
Officers were called to John Wilson Street in Woolwich, south east London, at around 2.20pm and the immediate area was shut down.
On its Twitter account, the Metropolitan Police helicopter team called the incident "serious".
A Scotland Yard spokesman said: "Officers have responded to an incident in John Wilson Street at 2.20pm today.
"We believe at this stage officers were called to reports of an assault."
A police cordon was set up around 100 meters around where the incident happened.
A white police tent had been put up in John Wilson Street close to the junction with Artillery Place and Wellington Street.
Two ambulances, two police cars could be seen in the road.
A picture posted on Twitter appeared to show three people lying in a street with concerned people around them.
Images also appeared to show knives and blood stains at the junction of John Wilson Street and Wellington Street.
Local residents said there was a heavy police presence in the area and most of John Wilson Street had been cordoned off.
David Dixon, the head teacher of the nearby Mulgrave Primary School & Early Years Centre, said he went into the street to find out what was going on after hearing of the incident.
"There were lots of police," he told the BBC. "I saw a body lying in the road. I went immediately back to shut the gate and to lock all the gates.
"The children were inside so they were as safe as possible."
All the traffic had been stopped and "there were gunshots after that," he added.
A woman working in an office overlooking the incident said: "I can see three bodies lying in the road with red blankets over them.
"All the bodies are within about 30 to 40 metres of each other. It looks like the police have covered them over because they must be dead.
"I didn't see the incident itself but I heard all the police and ambulance sirens, and then I saw an air ambulance landing nearby.
"I could see armed police all over the place. There was a lot of commotion, police running around in all different directions, as if they were looking for other people.
"I've been told that a man was attacked with a machete."
London Air Ambulance confirmed a doctor and a paramedic were sent to the scene at 14.27pm and remained on site.
London Ambulance Service was also called to the scene.
A spokeswoman for London Ambulance Service said: "We were called a 2.20pm to reports of an incident at John Wilson Street.
"We sent two responders in cars, three ambulance crews, two duty officers and London Air Ambulance were called out.
"We still have staff at the scene."
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