'This sucks,' says the American pilot of an A10 Thunderbolt tank buster when he realises that he has just unleashed a devastating cannon burst on a British armoured patrol. 'We're in jail dude,' chokes his wingman as they return to base, streaming expletives about their deadly mistake.

Jail is not where these dudes landed after they fatally strafed their British allies in Iraq in a tragic case of blue-on-blue just after the invasion. The senior officer was subsequently promoted to colonel, awarded the bronze star and now trains other American pilots in ground-attack. The recording is chilling. Gung-ho American reservists on their first combat mission are misled into thinking that there are no 'friendlies' in the area. Eager for action, they talk themselves into thinking that the orange panels marking the tanks as their British allies are enemy rocket launchers. They retch and curse when they are told that they have made a horrific blunder.

The incident itself was terrible enough, but this is not what has done most damage to Anglo-American relations. The Pentagon obstructed the inquest into the death of Lance Corporal Matty Hull. His widow has had to wait four years until someone leaked the cockpit recording to find out how her husband was killed. The Ministry of Defence appeared unwilling to stand up to its American counterparts and dissembled about whether video footage of the attack existed. Not for the first time, Britain is made to look like a subservient satellite taken wretchedly for granted by the country that is supposed to be its closest ally.

Opponents of the war in Iraq get daily vindication that the invasion was a terrible mistake. Supporters of the removal of Saddam feel betrayed by the appalling mess the divided and incompetent Bush administration has made of the aftermath. Tony Blair is an increasingly lonely voice when he pleads that Britain and America must remain each other's indispensable allies. 'We shouldn't give that up in any set of circumstances,' the Prime Minister declared when he appeared before senior MPs last week. 'The relationship with America is what opens lots of doors everywhere.' He did not make his case more persuasive when he selected climate change as an example of what he had got out of his closeness to George W Bush. When he leaves Number 10, his successors will have to fashion a new foreign policy for Britain which recasts its relationship with America and reorients its approach to the rest of the world.

The United Kingdom and the United States will remain firm friends. Their histories, economies and cultures are too entwined for it to be otherwise. They will continue to co-operate in the struggle against Islamist terrorism. Often, they will have mutual interests which will put them on the same side in global arguments.

That said, the relationship will never be the same again. And Tony Blair is one of the reasons why it will change. He has not been the Prime Minister he expected to be. He entered Downing Street as an instinctively pro-European leader who thought it was his destiny to settle Britain's relationship with Europe. He ends his premiership with it most defined by his relationship with the United States. The guiding principle of Mr Blair's foreign policy has been to get as close as he could to the American President, whoever he was. He was Bill Clinton's closest chum, then George W Bush's best buddy. As Mr Blair acknowledges, he has paid a high 'political penalty' for that. What he or Britain got in return is not clear, even to some of his closest colleagues. 'Iraq has been a total disaster,' says one minister who can be normally counted as a great Blair loyalist.

One of the unintended consequences of his adherence to America is to make it more likely that his successors will put some distance between themselves and Washington. Gordon Brown talks coolly, if imprecisely, about adopting a stance which puts 'Britain's interests first'. David Cameron has described himself as 'a liberal conservative rather than a neoconservative' who would be 'solid but not slavish in our friendship with America'. A Conservative government would not join those who believe in 'recklessly poking the United States in the eye', but nor would it be 'America's unconditional associate in every endeavour'. Mr Cameron is not anti-American. Neither is Gordon Brown. But they do sense the demand in Britain for our own declaration of independence from America.

Globescan regularly conducts a massive poll of attitudes towards the United States by sampling the opinion of 26,000 people across 25 countries. The latest survey finds antagonism towards America at an intense pitch. Even in countries such as Poland which are traditionally warm towards the US, public opinion has turned very sour. Britain is becoming almost as anti-American as France has historically been. Just a third of Britons now regard the United States as a force for good. Even if a future Prime Minister could convince himself that it would be sensible to do another Iraq, he would have huge difficulty persuading his colleagues or the public that he had not gone mad.

Tony Blair has been fixated with Washington because his guiding belief is that Britain maximises its global influence by flying as wingman to America. That role will seem less attractive to his successors for several reasons. One is that American power is going into decline. Sure, for the foreseeable future, the United States will remain a colossal military force, but its relative global clout will diminish as this century gets older. Iraq has already made the United States look much weaker in the eyes of the world. It has been a sanguinary lesson in the limitations of 'hard' power. Even some of the architects of the 'surge' plan don't believe that George W Bush's last throw is going to pacify Baghdad. Even under Tony Blair, American and British priorities are diverging. As the United States pours more troops into Iraq, Britain is desperate to get its soldiers home.

Immense damage has also been done to America's 'soft' power - the capacity to influence the world by example and persuasion. Uncouth Nation is a new book which explores rising anti-Americanism. Its author, Andrei Markovits, a professor at the University of Michigan, deplores the phenomenon, but that doesn't inhibit him from detailing its increase and its consquences. 'It matters that teenagers in Saudi Arabia, Bahrain, South Korea, Mexico, China, Taiwan, Lebanon, Pakistan, Nigeria and Argentina have come to despise America and the American people despite - or precisely because of - their being eager consumers of American culture.' The greatest antipathy is directed at the American President. As Markovits has it: 'Bush represents to Europeans the quintessential ugly American: arrogant, uncouth, uncultured, ignorant, inconsiderate, and aggressive.'

The departure of George W Bush may soften some of the hostility towards America. What it won't do is change the deeper, underlying trends which will demand a British foreign policy that is less exclusively concentrated on the relationship with the White House. Masked by the narrow and furious focus on the Middle East of the last few years, the tectonic plates of geopolitics are shifting. For a brief period after the fall of the Berlin Wall, American was an unchallenged hegemon, the only superpower - 'the hyperpuissance,' in the phrase of a French Foreign Minister.

The world is becoming increasingly multipolar and more reminiscent of the competing Great Powers of the 19th century. Russia has just announced that it is going to exploit its economic revival to rebuild its military strength. China is constructing a blue-water navy, demonstrating the capacity to shoot satellites out of space and buying up vast tracts of Africa in order to use the continent's oil and minerals to feed Chinese economic growth.

Brazil and India are also achieving the growth to enable them to become the world powers that their geographical and population size say they should be. In this new world order, America will be less focused on its old friends across the Atlantic and more geared towards making alliances and confronting threats in the Pacific and Asia.

The world's most powerful economic group has been the G7: America, Japan, Germany, Britain, France, Italy and Canada. Sometime around the middle of this century, it is very probable that the G7 will be surpassed by the combined economic power of the BRICs - Brazil, Russia, India and China. That will be a decisive shift of global clout from the old West to the new powers of the South and the East. Gordon Brown talks readily about the challenge of India and China, but he has yet to provide details of how he would recast British foreign policy to deal with it. All the effort he has put into debt relief and good governance in Africa is undermined when China is supplying huge loans with no human rights strings attached.

Both he and David Cameron will have to think about how to re-energise Europe as a world player and reinvigorate Britain's relationship with her closest neighbours. On the Chancellor's recent trip to India, there was a telling moment when the Indian Prime Minister greeted him as a 'leader of the EU'. That is not how Mr Brown, who has a reputation as a grudging European, is accustomed to thinking of himself. The Tory leader's attempts to build relationships in the EU is handicapped by his party's atavistic hostility to everything European.

Global institutions which reflect the balance of world power as it was in 1945 will have to be radically overhauled. It will become ever harder to justify Britain's possession of a permanent seat on the UN Security Council when Brazil and India do not have one. The big issues of this century - none of them more important than climate change - cannot be addressed by a foreign policy obsessed only with hugging Washington. The challenge for Tony Blair's successors will be to embrace the whole of a rapidly changing world.