Terrorism returned to the streets of Britain yesterday when a soldier was murdered by two suspected Islamists who attempted to behead and disembowel him as he left a barracks, in the first deadly attack since the 2005 London bombings.

One of the suspected killers, who addressed an onlooker who had a camera, said the pair had carried out the attack "because David Cameron, [the] British government sent troops in Arabic country".

As pedestrians stood close by the armed men, he went on: "We swear by almighty Allah we will never stop fighting you," according to footage obtained by ITV News.

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The Independent understands the dead soldier – who was wearing a Help for Heroes T-shirt – was a member of the Royal Regiment of Fusiliers, which is currently based overseas. He was ambushed by the men as he left the base in Woolwich, south-east London, who attacked him and then dragged his body into the middle of the road to pose for photographs while standing over him waving a cleaver and a gun, according to witnesses.

Senior Whitehall sources today confirmed to the BBC that the man who had been killed was a member of the armed forces.

Mr Cameron was cutting short a meeting with European leaders to chair a meeting of the emergency committee Cobra this morning as police and security services investigate whether the two men – later shot and wounded by police – were working alone or as part of a bigger group.

"It's the most appalling crime," he told reporters in Paris. "We are obviously urgently seeking the full facts but there are strong indications that it's a terrorist incident."

He said that they were looking at every aspect of security for troops across Britain, but he added: "The best way to defeat terrorism is to make sure you continue to live your life and make sure that terrorism never wins."

The London Mayor Boris Johnson added: "This afternoon's attack in Woolwich is a sickening, deluded and unforgivable act of violence."

Only hours after the attack was carried out, video footage of one of the suspected killers emerged. With his hands bloodied and carrying a cleaver, he is seen telling the bystander with a camera: "I apologise that women had to witness this today but in our lands our women have to see the same. You people will never be safe. Remove your governments – they don't care about you."

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The man, who spoke English without a foreign accent, then saunters back across the road towards his victim lying in the street to join his apparent accomplice. The two men made no attempt to escape and charged a police car carrying an armed response team when it arrived at the scene about 15 minutes after the killing, according to a witness.

"The black guy ran at them with a meat cleaver before it stopped and he was right by the car when they shot him," said Julia Wilders, 51, who lives close by. The second man, who had a gun, was also shot, she said.

The men were taken to separate hospitals by air ambulance and they were expected to survive despite their injuries, according to police last night.

The men were believed to have waited outside the Woolwich barracks of the 2nd Battalion, the Princess of Wales's Royal Regiment, which has deployed to Afghanistan and Iraq, where one of its members, Sergeant Johnson Beharry, won the VC.

Military sources said the soldier had left the barracks by car, but witnesses indicated that he was rammed while walking along the road in an apparently pre-arranged ambush, before being attacked while he was propped up against a wall of a block of flats.

One witness, identified only as James, said he and his partner saw two black men attack a young man aged about 20 with kitchen knives like he was "a piece of meat".

"They were hacking at this poor guy, literally," he told LBC Radio, adding that a group of brave women tried to shield the soldier from the two men.

"They were hacking at him, chopping him, cutting him. 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."

Children returning from a school trip were kept locked inside nearby Mulgrave Primary School while the police operation played out.

One local woman said she thought she saw one of the suspects preaching in Woolwich town centre about a week ago. Her daughter, Rebecca France, 18, said yesterday: "It was really political and angry. She said she thought it was strange because he was different from the usual guys who preach in the name of Jesus – he wasn't doing that."

The Muslim Council of Britain said the use of "Islamic slogans" indicated they were motivated by their faith. A statement from the council said: "This is a truly barbaric act that has no basis in Islam and we condemn this unreservedly. Our thoughts are with the victim and his family. We understand the victim is a serving member of the armed forces. Muslims have long served in this country's armed forces, proudly and with honour.

"This attack on a member of the armed forces is dishonourable, and no cause justifies this murder."

Police had set up a series of cordons around the scene last night with extra police patrols in the area and helicopters crossing the skies overhead. The Independent Police Complaints Commission said it sent 12 investigators to the scene to investigate the police shooting after reports of at least six shots being fired.

Shortly before 10pm last night the Metropolitan Police Commissioner, Sir Bernard Hogan-Howe, confirmed the murder investigation was being led by Counter Terrorism Command with two men arrested. He added: “It is hard to comprehend the shocking and horrific scenes we have seen this afternoon on a busy street as Londoners went about their day as normal.”

Last night there were clashes between EDL supporters and police in Woolwich after officers surrounded the local Islamic centre.

Islamists have threatened a number of times to behead a British soldier in retaliation for involvement in wars in Afghanistan and Iraq. Six years ago a group of British Pakistanis based in Birmingham were convicted of plotting such an attack and their leader, Parviz Khan, received a life sentence.

Khan admitted planning to lure a soldier off the streets then film the beheading.

He was described in court as having the "most violent and extreme Islamist views" and his aim was to deter any Muslim from joining the British Army.

Video: Woolwich attack - man with bloodied hands and knife addresses camera

WARNING: Contains graphic images