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LONDON (CNN) — They first hit the man, thought to be a British soldier, with a car in broad daylight. Then the two attackers hacked him to death and dumped his body in the middle of a southeastern London road.

As the victim — dressed in what appeared to be a T-shirt for Help for Heroes, a charity that helps military veterans — lay prone, one of the two attackers found a camera.

“We swear by almighty Allah we will never stop fighting you,” said a meat-cleaver-wielding man with bloody hands, speaking in what seems to be a London accent.

“The only reasons we killed this man this is because Muslims are dying daily,” he added, in video aired by CNN affiliate ITN. “This British soldier is an eye for an eye a tooth for tooth.”

One witness, Michael Atlee, described the gruesome, frenzied and ultimately fatal sequence of events Wednesday afternoon as “a bloody mess.”

British Prime David Cameron called it a terrorist attack.

“We will never buckle to terror,” Cameron wrote on Twitter.

Home Secretary Theresa May offered a similar assessment Wednesday night of the situation and a similar message of resolve.

“We have seen terrorism on the streets of Britain before, and we have always stood against it,” she said. “Despicable acts like this will not go unpunished.”

‘They were just animals’

A witness, who identified himself only as James, told London’s LBC 97.3 radio station that he saw two men standing by the victim, who was on the ground in the British capital’s Woolwich neighborhood.

At first James thought they were trying to help the man. But then he saw two meat cleavers, like a butcher would have.

“They were hacking at this poor guy, literally,” he told the radio station, as if they were trying to remove his organs.

“These two guys were crazed. They were just not there. They were just animals.”

Afterward, the men appeared to want to be filmed, with one of the attackers going over to a bus and asking people to take photos of him as if he wanted to be on TV.

In video obtained by British tabloid newspaper The Sun, a cleaver-wielding man apologized to women who had witnessed the attack, then quickly added “but in our lands our women have to see the same.”

“You people will never be safe,” he said. “Remove your government. They don’t care about you. You think David Cameron is going to get caught in the street when we start busting our guns?

“… Get rid of them. Tell them to bring our troops back so we can all live in peace.”

Police responded to the assault soon after it was reported at 2:20 p.m. (9:20 a.m. ET). They included armed members of a firearms unit, even though British police typically don’t carry guns, because “early reports” indicated the attackers had “weapons,” Metropolitan Police Commander Simon Letchworth said.

The suspects rushed at the arriving officers before being shot, James told the radio station.

“They have both been taken to separate London hospitals and are receiving treatment for their injuries,” Letchworth said.

Centuries-old barracks part of London neighborhood

Cameron — who was in France at the time of the incident but headed back home promptly — declined to confirm if the man killed was a serving soldier, while Britain’s Defense Ministry said it was investigating to see whether that’s the case.

Yet Nick Raynsford, a member of Parliament, told CNN that the victim is believed to be a serving soldier who was based at a nearby barracks.

The soldier had apparently been on duty in central London and was returning to the Royal Artillery Barracks in Woolwich when he was attacked, Raynsford said.

The MP described Woolwich as a mixed, multicultural area, adding that troops stationed at the centuries-old military barracks there have a close relationship with locals.

Even as they worked to piece together what happened and why, British authorities beefed up security Wednesday around Woolwich and all military barracks in London, according to a British government source.

And British Defense Secretary Philip Hammond said the killing was a “very shocking incident” and that the United Kingdom takes the safety of its troops “very seriously,” as he headed into Wednesday night to a meeting of the country’s civil emergency committee known as COBRA.

One suspect’s video statement justifying the attack spurred the Muslim Council of Britain to issue a strong statement condemning what it called “a truly barbaric act that has no basis in Islam,” as well as to urge Muslim and non-Muslims alike “to come together in solidarity to ensure the forces of hatred do not prevail.”

The bloodshed spurred swift condemnations elsewhere in Britain as well — from a “concerned” Queen Elizabeth II, to London Mayor Boris Johnson’s description of a “sickening deluded and unforgiveable act of violence,” to Labour Party leader Ed Miliband’s prediction that the “whole country will be horrified.”

That’s certainly true for Lauren Collins, who saw the gore up close.

“I still am quite shaken at what I’ve seen,” she told CNN. “I’ve seen a victim of an awful attack, and I’ve seen a body of a young man.”