After two men butchered a British soldier in broad daylight Wednesday cameras captured them uttering: "We must fight them as they fight us. An eye for an eye, a tooth for a tooth,” said one.

And when a bystander, who had gotten off a bus to intervene, knelt before the wounded soldier, she said one of the perpetrators urged her to step back. "He said 'don't touch, I killed him.' I said 'Why?'” she recounted to the British press. “He said 'He's a British soldier. He killed people. He killed Muslim people in Muslim countries.'"

Their violent act, the first suspected terrorist attack on British soil since the 2005 suicide bombings in London that killed 52, is certainly rare. But some fear that their apparent motive – that US-led foreign policy in Iraq and Afghanistan is an attack on Islam – could become a more prevailing viewpoint among the disenfranchised Muslims of Europe.

Muslims here in France have been ambivalent about European foreign policy. The US “war on terror,” supported by European allies to varying degrees, is harshly criticized, but none would call France or England, for example, “anti-Islamic,” says Farhad Khosrokhavar, a sociologist at France’s School of High Studies in Social Sciences. “But the majority of Muslims in Europe are economically fragile. Existentially, they feel they are excluded and feel the pinch of everyday life. A very tiny portion of them get radicalized, but it can have catastrophic results.”

Two British men, born to Nigerian immigrants, approached soldier Lee Rigby, a 25-year-old father, on Wednesday afternoon on a London street outside the Royal Artillery Barracks in Woolwich and hacked him with knives and a meat cleaver. Instead of fleeing, they lingered after the attack, claiming to have acted in revenge for wars waged in Muslim countries.

Today, British officials have reported that the two men, one of whom converted to Islam a decade ago, were known to security officials for alleged extremist activity.

The attack comes a month after the bombings at the Boston marathon and a year after Mohamed Merah attacked French army personnel and then shot into a Jewish school, killing three children in Toulouse, France. The attack has raised fear of "lone wolves" who are not part of networks such as Al Qaeda but act on their own. While such low-grade plots generate far fewer casualties than attacks like 9/11 they are also harder to stop.

Gilles Kepel, an expert on Islamist movements at SciencesPo in France, draws a connection between the three recent acts as examples of “third generation” jihadism, a bottom-up waging of terrorism that can be carried out inexpensively and without the kinds of networks that leave traces, but that nevertheless are broadcast around the globe. In addition to frightening people, it also provides an example for new recruits.

“It will lead to reactions against Muslims,” he says, such as the closing of mosques, “which will help create a paranoid feeling among mainstream Muslims, so more and more are alienated from European societies.”

'They confuse the issues'

That alienation is something that is increasingly on the radar in Europe, as the continent has been mired in economic stagnation and far-right groups have surged in polls – many of them condemning immigration as a threat to European society.

“There is a growing sentiment of alienation among some radical and disenfranchised Muslim youth in Europe, who are aggrieved by their difficult social and economic integration, but also mention the wars in Afghanistan, Iraq, and Mali, the Israeli-Palestinian problem, as well as the drone attacks,” says Karim Bitar, a senior research fellow at the Institute for International and Strategic Relations in Paris. “They tend to confuse all the issues, and to see everything through the lens of a war on Islam.”

This latest attack, he says, will be adopted by far-right groups as another reason to fear the so-called “Islamization” of Europe. Just this week, a far-right historian in Paris killed himself at the altar of Notre Dame Cathedral, after writing a text railing about gay marriage and the displacement of French society by immigrants.

“This crime will provide fodder to the propaganda of the extreme right and populist movements in Europe who also confuse all the issues and also analyze everything through the lens of a culture clash,” says Mr. Bitar. “Far-right rhetoric reinforces this phenomenon [of alienation]. It reinforces their belief that they are not welcome, not part of this society.”

Jonathan Laurence, a Boston College professor and author of The Emancipation of Europe’s Muslims, says the worst impact will be the distrust that grows in the wake of such attacks, "the everyday suspicion that it exacerbates,” he says. “It’s not a question of whether it’s justified or unjustified, it’s part of the logic of the terrorism theater.”

Opposition to the 'war on terror'

A 2006 poll from Pew showed the US “war on terror” as extremely unpopular among Muslims in Europe, with 83 percent of Muslims in Spain opposed, 78 percent in France, 77 percent in Britain, and 62 percent in Germany.

Three years later, a survey of British Muslims for BBC showed that 75 percent said it was wrong for the “West” to intervene militarily in Pakistan and Afghanistan – though a majority, 78 percent, also said that they opposed Taliban attacks against NATO soldiers.

“I think many Muslims feel a sense of concern with fellow Muslims in different countries, when Muslims are suffering from interventions from outside,” says Paul Weller, a professor of Inter-Religious Relations at the University of Derby in the UK. “But that is distinguished in relation to Islam, the religion. So that not all Muslims would feel there is an attack on Muslims would necessarily consider it an attack on Islam.”

Taj Hargey, imam of the Oxford Islamic Congregation and director of the Muslim Educational Centre of Oxford, says he does not feel that invasions have been an attack on Islam, but that they've given rise to terrorism. “We never had any form of Muslim violence or terrorism until the UK engaged in an illegal war in Iraq,” he says.

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But some Muslims are hesitant to be so open about criticizing foreign policy – a dangerous path, says Dr. Weller. “In a healthy democracy, it’s very important that Muslims don’t have to feel, ‘oh, we are happy with foreign policy,’ when actually a lot of non-Muslims are not very happy with foreign policy,” he says. “Muslims shouldn’t have to be more loyal in their protestations of X, Y, and Z than other members of society.”

Bitar says many Muslim groups feel pressure to publicly condemn terrorist attacks but it’s a requisite that many resent, since they feel “it goes without saying that they are opposed,” he says. “When the KKK does something, not every white organization feels compelled to condemn it.”