Tony Blair may be puzzled by the two key findings of today’s Times poll. They show that nearly two thirds of Britons believe his decision to go to war in Iraq heightened the risk of terrorist attacks in London. But they also give him the second-highest personal rating of his entire period in power. Puzzlement, however, would be out of place. Experience suggests the Prime Minister might equally react to these two numbers with a sense of vindication, and on this occasion he would be right to do so. The highest poll ratings of his career remain those taken immediately after the invasion of Iraq. They then slumped. The most obvious interpretation of his ratings recovery is that he has now been forgiven by many who opposed the war. It also shows that Britons are ready to distinguish, as history will, between two largely separate threats to international security that have convulsed the world over the past four years. One, posed by Saddam Hussein until 2003, may have been exaggerated by the available intelligence but nonetheless left responsible leaders with difficult decisions. The other is the threat from terrorists, who claim to be Islamic, but are self-obsessed, nihilistic thugs. They are linked — but mainly by geography — in the continuing carnage wrought by suicide bombers in Baghdad.

The fact of Britain’s role in the invasion and occupation of Iraq clearly cannot be ignored as a consideration in this month’s bombings in London. But to see in them a simple, avoidable case of cause and effect — as some politicians who should know better, and others who plainly do not, have done — encourages in their listeners a grotesque confusion of reason and justification. It also bespeaks dangerous amnesia as to the recent, bloodsoaked history of terrorism carried out in the name of jihadi Islam.

In the aftermath of the bombings of July 7, Mr Blair insisted they had “nothing to do” with Iraq. If he erred, it was in exaggerating to make the point that real blame for any such atrocity lies with its perpetrators. By the same token, real hope for preventing its recurrence lies only with understanding how those perpetrators’ grievances have metastasised into such a lethal cult of suicide and murder. The answers involve the confluence of a mediaeval ideology with the 21st-century technologies that disseminate it with little expense or effort to every possible convert on every continent. The process that led to July 7 and the botched follow-up last Thursday began long before April 2003, and its target list is far, far longer than that of London’s Underground stations.

The argument that London would be safe but for Britain’s presence in Iraq is almost too flawed to take seriously. If the British forces currently serving there had toppled an Islamic government and were deliberately targetting innocent Muslims for their perverted gratification, it would have some merit, but the opposite is true. Britain helped to remove a fundamentally irreligious dictator whose hero was Stalin (his collection of biographies of the Soviet leader was envied even by Russian scholars) and whose Baathist creed was based on the explicit rejection of Islam in favour of pan-Arab nationalism as the chosen vehicle for Iraq’s propulsion to regional hegemony. He did profess to embrace Islam as his grip on power loosened, but only out of blatant opportunism. Osama bin Laden, for one, was not taken in. It was he, after the invasion of Kuwait in 1990, who called on Saudi Arabia to liberate the country before the US did, and then offered to undertake the task himself. Bin Laden’s main gripe was the presence of US troops in Saudi Arabia — they have since left and yet the terrorism has intensified.

Nor is the new Iraq, for all its agonies, an enemy of Islam. On the contrary, its best hope for the future is of benign dominance by its Shia Muslim majority, and its de facto kingmaker as the interim government prepares for the next round of elections is the country’s leading Shia cleric. Al-Qaeda, were it a genuinely religious movement, could have hoped for no better outcome from the invasion. Instead, bombers acting in its name have murdered vast numbers of Islamic men, women and children since the January elections, which paved the way for an Islamist-dominated Government.

There is no question, of course, that the flatteringly named Iraqi “insurgency” has become a global rallying cry for militant Islamism. But the world is not short of such recruiting sergeants. The Bosnian war served the same purpose in the mid-1990s, even though the US led the international relief efforts. The Israeli-Palestinian conflict continues to do so, as does the Chechen one. There are Muslims with grievances that the wider world may have been slow to address. But such causes do not include the creation of a new Islamic caliphate for the third millennium stretching from Casablanca to Kashgar (or from Luxor to Leeds) in which Sharia law would obtain everywhere and absolutely, and women would enjoy all the rights their Afghan sisters may recall from the era of the Taleban. This violent vision, the closest thing militant Islamism has to a concrete political goal, is explicitly endorsed by extremist groups and owes its currency to a constant stream of digital demagoguery.

It would be absurd to blame the current surge of terrorist attacks on the internet. Yet there is no doubt that the marriage of modern technology and malevolent medievalism has expedited the spread of hateful and hysterical propaganda wherever governments have not acted forcefully against the propagandists. Open societies must find ways of modulating public discourse without losing the openness that defines them. And there must be a clearer understanding that there will always be new causes for these extremists: the emancipation of women; the West’s acceptance of homosexuality; the very existence of moderate Muslims, in Iraq and here, who are, in their moderation, “apostates”.