"When the banner unfurls, all reason is in the trumpet." — Ukrainian Proverb
(1) A full text of Mr. Cameron's remarks was not readily available on line; at least I couldn't find one. Videos of people commenting, embedded tweets, quotations in news stories — yes; a simple transcript: no, at least not before a whole lot of other words and images got out, and pretty effectively buried in them.
(2) I think Mr. Cameron, certainly many of the news reports, settled on "the Islamic State" for the name of the terrorists moving into a guerilla army who originally called themselves, in English, "ISIS": Islamic State in Iraq and Syria. Let's stick with "ISIS": It's an easily-remembered word; it's the name of an important Egyptian goddess — which should be an abomination for an Islamist fanatical sect — and it's what we started with. Calling people the name they wish to be called is a sign of respect; getting people to call you how you want to be called, and changing it periodically, can be an exercise of power. ISIS should be respected only in the sense of recognition of their potential to trigger upheavals; other than that they should be condemned and contemned and not granted power, not in any way, starting with vocabulary.
(3) If I heard right and remember right, Mr. Cameron referred to the method of the murder of Mr. Haines as peculiarly horrible and gruesome. I haven't watched the videos, but judging by the knife in the hand of the murderer, the "execution" would not have been elegant. We should remember, however, that beheading in England for centuries was the merciful method of execution, reserved for the genteel, noble, and royal, and not always for them. Starting with the reign of Edward I, those convicted of "high treason" — and "treason" could be broadly defined — were hanged, drawn, and quartered. Under Henry VIII and after, poisoners were boiled alive, and heretics were burned at the stake. The routine method of execution in England was "to be hanged by the neck until dead," which into the 19th century meant exactly what it said: death by strangulation. The major issue is not the method, but the fact of killing someone; still, it is significant that Islam was historically merciful in requiring beheading for executions, and highly significant that eliminating executions by torture as public instruction and entertainment was primarily a gift of the Enlightenment.
(4) Following a standard line I approve of, Mr. Cameron described ISIS as unIslamic, in large part, he said, because Islam is a religion of peace. Not exactly. In one mainline tradition of Islam, peace was very effectively, all things considered, maintained within the realm of Islam, whereas warfare was directed outward: which was standard for most of human history. As a quick reading of the Books of Joshua and Judges in the Bible will indicate, the tradition of Holy War was long accepted in the sister Religions of the Book — Judaism, Christianity, and Islam — and followers of all the gods from Marduk on have usually been able to bring some god to their side when they wanted to drum up enthusiasm for conquest. As the Mongols under Genghis Khan showed spectacularly, the gods aren't necessary for mass slaughter, but religious motivation can indeed be an effective motivator. Religions of any antiquity are complex enough be used to foster peace, or war, and for the very long period in which "warlike" was a compliment, Islam was honored, among the conquerors, for bringing Muslims victory.
ISIS should be resisted across the board, starting with not accepting the "Islamic State" as a caliphate ruling by right more than what they currently and tentatively control by force of arms — and can be thrown out of: parts of Iraq and Syria. So let's use the pagan acronym and pronounce it "Isis." And if we shouldn't give them power to jerk us around with new names, we certainly shouldn't allow them to manipulate the foreign/military policy of the great powers by blatantly provocative YouTube postings.
ISIS itself is a threat to American and British and, far more directly, Muslim individuals: especially, with Westerners, to those doing good and necessary work as journalists and aid workers. ISIS, however, is not a threat to America or Britain; no terrorist group is, not even when they kill thousands. The USSR lost millions in World War II and still survived; it's nothing you want to go through, but "an existential threat" to individuals just isn't an existential threat to nation-states.
What is a threat to the world is ISIS as not being peculiarly barbaric in their methods. Their cruelty was commonplace and widely accepted before the humanitarian revolution of the Enlightenment and following, and it is a cruelty that can be fallen back into all too easily.
The Amish and other peace churches practice a "religion of peace" and some Sufis and others; and there are secular pacifists. But serious pacifists are not numerous, and if we are not very careful, ISIS will provoke civil war in the Muslim world and crusades against itself. They will remind us that "______ is a religion of peace" is a statement that needs a lot of hedging for any faith, definitely with faith-communities for whom "crusade" is a positive term.