The London bombings, which killed more than fifty people and wounded more than 700, were despicable acts that, like those in Madrid, Bali, the United States and elsewhere, have rightly been condemned by all decent people. But British Prime Minister Tony Blair’s claim that the chief motivation of the terrorists was “a desire to impose extremism on the world” rang as hollow as George W. Bush’s claim after the September 11 attacks that Islamic terrorists “hate our freedoms.”

The rationale for the London attacks appeared plain enough, whoever bore direct responsibility. A previously unknown group calling itself The Secret Organization of Al Qaeda in Europe claimed that the bombings–which officials in London said had been carried out by British-born Muslims–were “in retaliation for the massacres that Britain is committing in Iraq and Afghanistan” and a punishment for Britain’s support for Israel.

Viewed in this context, the bombings are another tragic reminder that Bush’s invasion of Iraq was an ill-conceived and counterproductive response to 9/11. Instead of helping to win the “war on terror”–a dubious concept–the invasion has become a source of increased Arab anger and Iraq has turned into a training ground for new terrorists, some of them likely drawn from the more than 20 million Muslims who call Europe home. (A classified CIA report completed in May concluded that Iraq might prove more effective than Afghanistan in preparing recruits for acts of urban terror because it provides real-world experience.)

Most Europeans never believed Bush’s lies about a link between Saddam Hussein and Al Qaeda and from the start wanted their governments to have nothing to do with Washington’s Iraq invasion. Belatedly, Americans, already disabused of the notion that Saddam had weapons of mass destruction, are beginning to understand the full extent of their government’s folly. For the first time since the US invasion, a plurality of Americans see Iraq as distinct from the “war on terrorism,” according to a USA Today/CNN/Gallup poll released just days before the London attacks. The same poll found that 53 percent now think the invasion was a mistake, and a plurality believe the war in Iraq has made the United States less safe from terrorism. They have good reason for that belief: According to RAND, the 5,362 deaths from terrorism worldwide between March 2004 and March 2005 were almost double the total for the same twelve-month period before the invasion, in 2003.

In the short term, Bush may be able to capitalize on the London attacks, to push through an extension of the Patriot Act, for example. But the attacks are also an occasion for critics of the war to raise anew questions about Bush’s real motivations in Iraq and to make the case for withdrawal.

Such a withdrawal, however, would be only a start toward correcting misguided policies. The London bombings should not be the beginning of a new phase of militarization against Islamic jihadism but of a new transatlantic partnership that works toward peace between Israelis and Palestinians, more economic opportunities for Muslims both in Europe and elsewhere, and an end to Western support of dictatorships in the Arab world. Unless and until we do these things, Michael Scheuer, who headed the CIA’s Osama bin Laden unit for nine years, told the Associated Press, bin Laden will “make us bleed enough to get our attention.”

That is the sobering lesson of London.