UPDATE from the BBC:
One witness, identified only as James, said two men had attacked another man, aged about 20, who was wearing a T-shirt of military charity Help for Heroes.
"These two guys were crazed. They were just animals. They dragged him from the pavement and dumped his body in the middle of the road and left his body there," he told LBC radio.
He said after the "horrendous" attack, the two men, who were also in their 20s, stood around, waving knives and a gun, and asked people to take pictures of them "as if they wanted to be on TV or something".
"They were oblivious to anything, they were more worried about having their photo taken, running up and down the road," he said.
'Shootings' and 'machete attack' in south east London: latest Telegraph,May 22, 2013
Woolwich stabbing / beheading in John Wilson Street SE18 Photo: @BietLe_
By Daily Telegraph reporters
17.46 Elliston House, a 21-storey block of flats near the scene, is being evacuated to allow police to perform a controlled explosion on a blue car parked in front of it.
17.43 The attackers shouted "Allahu Akbar" (the Arabic expression meaning "God is Great"), according to Whitehall sources - BBC News.
17.41 An Army Cadet force that meets at the Woolwich barracks messages its members telling them not to arrive at the barracks in uniform.
A message posted on their community organisation public Facebook page at around 5pm says: "In light of current events outside the Artillery Barracks in Woolwich I am advising all cadets and staff to travel to the unit tomorrow night in full civilian clothes. Time will be given for cadets and staff to get changed into uniform when you arrive."
17.38 Prime Minister David Cameron describes the killing as "truly shocking", the Press Association reports.
17.35 The killing was likely to be a politcally motivated Islamist terror attack, sources tell Sky News.
17.31 & lt;noframe>Twitter: Nigel Fletcher - Very alarming reports of what has taken place here in Woolwich. My thoughts are with those affected by this very serious incident.</noframe>
17.28 Theresa May, the Home Secretary, has summoned a Cobra meeting, the BBC reports. The meetings are held when the Government is dealing with an emergency.
17.23 The Ministry of Defence says it is urgently looking at the reports that the incident involved a soldier. The incident occurred some 200 yards from the Royal Artillery Barracks, adjacent to Woolwich Common, the historical home of the Royal Artillery.
The barracks, also known as the Woolwich station, now houses a number of the King's Troop Royal Horse Artillery and independent companies of the Grenadier and Coldstream Guards.
17.14 The witness who spoke to LBC, called James, says there were "brave women" present who were shielding the victim at the scene.
He tells the radio station: "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.
"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."
17.08 Julia Wilders, one of the witnesses, adds: "There were two black guys that looked like they were trying to resuscitate a white guy on the floor.
"I thought there'd been an accident but then I saw they were using meat cleavers to hack him up.
"We live just behind where it happened and once we got back we walked back to have a look and that's when I saw one of the black guys pull out a handgun.
"My husband screamed at me to get back. I was petrified.
"As I was running back I saw the police pull up and the black guy was running towards the police car and they shot him."
17.04 Another witness, Shane Webb, 48, an electrician who lives in a tower block overlooking the scene, says he looked out of the window of his flat after hearing a loud bang.
He says: "There was a white man lying in the middle of the street. He was definitely dead. He was wearing a bomber jacket.
"As I was watching a police car pulled up and two cops got out. They both just raised their guns and fired. There were about five or six shots very fast and one of the black guys just went down. I don't know if he was dead or not, but he just collapsed, just went down.
"They were firing at both of them and I think the other was hit as well, but I couldn't see that very well."
17.02 The Independent Police Complaints Commission, which is called in when ever firearms officers shot people, says it is investigating.
16.58 Julia Wilders, 51, who lives nearby, says: "My husband saw what he thought were two men trying to resuciate another man so we went to see if we could help.
"Then we saw a black guy with a gun. We went up to the school and told them and they closed it down.
"I went back to the scene and saw the two men. One had two machetes and the other had a machete and a gun.
"The man with two machetes ran at the police when they arrived and the police shot him. I saw him fall.
"The other one looked like he was goiing to go for his gun. so they shot him too.
"The two men were just dressed in normal clothes. They were shouting but I couldn't make out what they were saying."
16.54 Nick Rainsford MP says the incident took place outside the barracks in Woolwich. He tells the BBC: "As a result of the incident one man is definitely dead.
"I believe that this is someone who is a serving soldier at the barracks. Two others who are regarded by the police as suspects have been arrested but in the course of the arrest they sustained serious injuries and are both in hospital.
"I don't know the background to the cause of the incident although I have been told it concerned a road traffic accident, but I haven't had that confirmed. I am told by the police that they took a number of weapons from the site including a firearm and knives and a machete."
16.46 Nick Rainsford, the local MP, says he spoke to the police borough commander and the commanding officer of the nearby barracks, who confirmed a soldier was the victim. He says: "My understanding is that one individual is dead as a result of a very serious incident involving at least three individuals.
"A number of weapons have been recovered from the site. There appears to have been gun shots.
"One individual who I believe to have been a soldier serving at the barracks has been killed. Two other individuals who the police regard as suspects were both seriously injured."
16.41 The incident is believed to have happened outside Mulgrave Primary School & Early Years Centre. David Dixon, the head teacher, tells the BBC there were gunshots fired. He says: “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.”
16.39 LAS confirm there is one man dead at the scene and two other men are injured. One of them is in a serious condition.
16.38 London Air Ambulance (LAS) confirms that one patient was airlifted from the scene, while another was taken away by road ambulance.
16.34 One witness, identified as James, says he and his partner saw two black men attack the young victim with knives, including a meat cleaver. The witness tells LBC: "They were hacking at this poor guy, literally. They were hacking at him, chopping him, cutting him. They dragged him from the pavement and dumped his body in the middle of the road and left his body there."
16.30 Eyewitnesses describe seeing two people shot in Woolwich, south east London, after armed police were called to an incident in which a man was attacked with a machete-style knife. He is said to have been wearing a Help for Heroes t-shirt and to have been dumped in the street.