It gets an outing on every visit of an American president to these shores. And yesterday's appearance of President George Bush in London, stopping by on his farewell tour of Europe, was no different. Both Gordon Brown and Mr Bush paid tribute to the "special" relationship between our two nations.

The "special relationship" is a concept that cuts little ice with hard-headed diplomats on both sides of the Atlantic. Yet it was once more than a platitude. While the default position of much of the world has traditionally been to look upon America with guarded scepticism, Britons (at least for the past century) have been instinctively well-disposed to the United States and its leaders. The bonds of a common language and a history of shared struggle in two world wars did indeed make this relationship something out of the ordinary.

So perhaps Mr Bush's most significant legacy, as far as Britain is concerned, will be the destruction of the instinctive trust of America and its leaders that once prevailed here. It is no exaggeration to say that Mr Bush has done more damage to relations between our two nations than any president in living memory. This rupture is not an accident of circumstance; there are no impersonal forces of history to blame. This sorry state of affairs is the consequence of the actions of a single leader and his small coterie of advisers.

America's invasion of Iraq must, of course, be recorded at the top of the charge sheet. In 2002, Tony Blair announced that he was prepared to pay "the blood price" for the sake of the special relationship. But it was not the then prime minister who paid it. That fate has, instead, fallen to 176 British troops who have lost their lives in Iraq.

Yet President's Bush's malign legacy is about much more than Iraq. Relations have been soured by the prolonged jailing of innocent Britons in Guantanamo Bay, the suspected use of Britain as a stopover point for CIA torture flights and a hopelessly one-sided extradition treaty. President Bush has even helped to undermine the peace dividend from the end of the Cold War. He has antagonised Russia by pushing America's missile defence shield project, an outpost of which is to be situated on British territory.

Of course, one might argue that the real culprit here is Mr Blair, who signed Britain up unquestioningly to President Bush's foreign-policy goals when he was in Downing Street. Mr Blair's burden of responsibility is undeniable. But it does not rescue Mr Bush from the abysmally low regard in which he is held by the majority of Britons. And with his disregard for international law, his arrogant refusal to build alliances, this President would have inspired fierce opposition here, even if Mr Blair had not committed Britain to the Iraq misadventure and the "war on terror".

In one sense, this is a discussion about history. Like all second-term American presidents, Mr Bush's power is waning by the day. His legacy will be for academics to debate. The pertinent question now is to what extent Mr Bush's huge unpopularity has contaminated wider public attitudes to America in Britain. Can a President Obama, or a President McCain, heal the wounds? Or is the damage permanent? One would have to suspect that the situation is recoverable; not least because America itself seems as eager for change as Britain. But whether the relationship will ever return to what it was pre-Bush, is another question entirely.

And whatever the future holds for transatlantic relations, there will be very few in this country who watched President Bush's plane depart yesterday without a feeling of profound relief that the end of this disastrous presidency is finally in sight.