For the first time since the bombing of the London Underground in 2005, the U.K. is reeling from a terrorist attack. The details of the killing in Woolwich, South London, are still emerging, but this appears to have been a highly personal, do-it-yourself-style assault that poses a special challenge to diverse societies such as the U.K.

The two killers -- at least one of whom was, according to the U.K. news media, a convert to extremist Islam of Nigerian descent -- hacked an out-of-uniform soldier to death near army barracks, using what appeared to be a meat cleaver and a knife.

Remarkably, the men remained with the body, their hands bloodied, to be filmed and photographed on a mobile phone as they explained their motives for the slaying to passers-by. One woman stood talking to the men for about five minutes. Locals milled around as the killers waited for the police to arrive.

It is possible that the men were connected to and directed by larger terrorist groups abroad. For now, though, they appear to represent what U.K. counterintelligence officials have long said is their growing fear: "lone wolf" terrorists, who are radicalized at home and plan attacks without having to communicate with terrorist groups or cells. They are, therefore, harder to detect and stop.

The men gave predictable, hackneyed justifications for the killing, namely that British soldiers should pull out of all Muslim countries. More interesting were the British accent of the man filmed and the confusion he showed about his own identity. He accused the U.K. military of killing "in our lands," referring to "our" Muslim countries. Seconds later he said the U.K. government should "bring our troops back," referring to "our" British troops. A witness who talked to the men said one of them told her he hoped "to start a war in London tonight."

These men, like the Tsarnaev brothers who are accused of carrying out the Boston Marathon bombing with homemade pressure-cooker bombs, appear to be more a part of the society they attacked than of the ones they sought to champion. The main threat they pose is to the integration of Muslims in the U.K.

This was highlighted in the immediate reactions to the attack. Riot police clashed in Woolwich with protesters from the ultranationalist and xenophobic English Defence League, who made their usual abusive threats against Muslims. Two men were arrested after they tried to attack mosques in different parts of the country.

The U.K. government and mainstream British Muslim leaders have been through this drill before, including in 2005 after British-born Islamist terrorists killed 52 people. Both are making the right statements to avoid inflaming anti-Muslim sentiment, with Prime Minister David Cameron describing the attack as "a betrayal of Islam and of the Muslim communities who give so much to our country."

Two further responses would help. The first is to stress that these men were local, if as reports in U.K. media and their accents suggest, the men were British. The second is to make it clear that their twisted version of Islam does not connect them to other British Muslims. No more, at least, than Anders Behring Breivik, the Norwegian who in 2011 murdered more than 70 people in the name of creating a mono-cultural Christian Europe, was connected to other Christian Norwegians.

Whatever the connections of the two men to extremist groups -- and there are numerous reports that they were known to U.K. intelligence services as radicals -- this attack may best be treated be seen as a hate crime, as much as an act of terrorism, and responded to accordingly.

(Marc Champion is a member of Bloomberg View's editorial board. Follow him on Twitter.)