The best causes sometimes have the worst propaganda. This week demonstrators are expected to protest against President George W Bush in London. Never mind that thousands of Iraqi children were dying every year under a sanctions regime exploited by Saddam Hussein until the Americans entered Baghdad. Never mind that the Iraqi dictator was a mass murderer, using chemical weapons against his own people. Never mind that some of the organisers of the Stop the War Coalition supported the Soviet Union in its inglorious heyday. And never mind that the United States is today, as in 1917 and 1941, the arsenal of democracy.

The demonstrators can be dismissed easily enough. Their response is as predictable as it is depressing. Like their CND forebears, they believe that in politics there can be no enemies on the left, only the right. The wider public antipathy to Mr Bush is more troubling. Certainly Donald Rumsfeld, his defence secretary, has been inclined to shoot from the hip. Post-war liberal Britain appears peculiarly allergic to the American right. Our own government’s mixed record in the run-up to the war has also tarnished the reputation of its visitor — the prime minister’s bravery in fighting his corner was sadly counterbalanced by the bureaucratic skulduggery revealed by Lord Hutton’s inquiry. The result, as our poll shows, is that the British are too ready to listen to the caricature: that Mr Bush is a dangerous, dim-witted warmonger.

This is a president who has engaged with the world when many predicted a new and dangerous American isolationism, particularly after September 11. He has recognised that terrorism is the prime threat facing the West and he has pursued a resolute strategy of defeating it. Unlike his predecessor, he has been prepared to risk the lives of American troops to drive that strategy forward. He may be pursuing the interests of America, but he is also acting in the interests of the free world. It has been said that this visit is an embarrassment to Tony Blair; that Mr Bush would have done him a favour by cancelling. That is nonsense. The prime minister is to be applauded for recognising the need to keep America engaged. That need has driven much of Britain’s foreign policy in recent times. This week’s ceremonials are part of that important process.

It would naturally be better if the situation in Iraq were more stable. But the attacks by a small number of determined Ba’athists and outsiders should not overwhelm the fact that progress is being made in restoring normality to the lives of Iraqis. Even so, the 400th American soldier has died, the post-war process has been muddled and the political pressures on the president are growing. His poll ratings at home have suffered despite the strongest economic surge for 20 years. In a year’s time he will seeking the support of the US electorate for a second term and that explains the renewed urgency about restoring Iraq to its people. Paul Bremer, the American administrator, met the country’s 24-member governing council in Baghdad yesterday to discuss a plan under which independence will be restored to the country as early as next June. If it works, the plan will be good for all sides. For Mr Bush, it offers the possibility of bringing the boys home soon — always a vote-winner. For the Iraqis, it offers the chance of democratic self-rule. As long as the process is not seen as a panic response to casualties, the omens are good.

It is easy to underestimate this president. Saddam did so, and so did the Taliban. The Europeans loathe him. Mr Blair has not made that mistake. He is aware that by supporting Mr Bush’s strategy to fight a long and difficult war on terror, he is looking after the interests of Britain. We, too, are in the front line. If Mr Bush is dismayed by some of the hostility he sees, he should console himself by taking the long view. Ronald Reagan, another right-wing Republican president, was also vilified in Europe. Yet his confident assertion of American power ended the cold war and brought real peace with the Soviet Union. Mr Bush’s critics should be heard but not appeased. History will vindicate him.