You will have your own view - there's so much to choose from - on which part of the open-mic conversation between George W Bush and Tony Blair at the Yo Summit was the most toe-curling. One of my favourite excruciating moments is when Bush thanks Blair for sending him a Burberry sweater as a birthday gift. The American President sends up the British Prime Minister by mocking: 'I know you picked it out yourself.'

There's no question which exchange is most enjoyable for those with contempt for the Prime Minister. It is the moment that makes Mr Blair look like the poodle of popular caricature. Worse, he comes over as a poodle who can't even beg his master to toss him a dog biscuit. It is the same bit of the encounter that has caused the most wincing among the Prime Minister's friends.

When Tony Blair offers himself as a Middle East peace envoy, he is casually rebuffed by the American President between bites on a bread roll. Told by Bush that 'Condi is going', the normally fluent Blair is reduced to inarticulate jabbering. 'Well, it's only if, I mean, you know, if she's got a... or if she needs the ground prepared as it were... Because obviously if she goes out, she's got to succeed, if it were, whereas I can go out and just talk.' Yeah, just talk.

It was awful for Tony Blair to be caught asking for permission to go to the Middle East. It was dire to hear George Bush saying he wouldn't let the Prime Minister of the United Kingdom go out - not even on a pointless trip. It looks even more humiliating when the French Foreign Minister is going.

In the build-up to the action to remove the Taliban in Afghanistan, George Bush was delighted to let Tony Blair go globe-trotting as an ambassador-at-large. The American President was happy to use Mr Blair in the same way on the road to war in Iraq. When it does not suit the White House, the Prime Minister of the United Kingdom is grounded.

The foreign policy realists in the British government will argue that a Blair trip to the Middle East would have no chance of achieving anything without American support. But that serves to underline a truth about Britain as an international actor which this country doesn't like to hear and Tony Blair doesn't want to tell. Britain has no independent leverage on any of the players in this crisis. When Sir Menzies Campbell pressed him to do more about the escalating conflagration in Lebanon, the Prime Minister replied testily: 'May I just point out that our influence with Hizbollah has been somewhat limited.' British influence over Israel, Iran or Syria is also 'somewhat limited'.

The only favour done to the Prime Minister by the broadcast of his rap with George Bush has been to illustrate a little of what he has been up against over the past five years in dealing with this American President. We have been frequently told by his defenders that, whatever verbal dyslexia he may display in public, the private Bush is as smart as a whip, with a sophisticated grasp of the complexities of the geopolitical situation. Analysing the carnage unfolding in Lebanon, the view of the American President is this: 'What they need to do is to get Syria to get Hizbollah to stop doing this shit and it's over.'

The unguarded mic also picked up the American President saying he didn't want to prepare any closing remarks for the G8 Summit. 'Just gonna make it up,' he shrugs. To the Chinese premier, he remarks, 'This is your neighbourhood.' They are in St Petersburg. Continuing his conversation with the Chinese leader, President Bush goggles: 'Russia's a big country and you're a big country,' like a seven-year-old who has just discovered them in the atlas.

That fragment of Bush and Blair will be an interesting specimen for future historians to examine when they try to assess British foreign policy under Blair. The question that he has wrestled with, just as his predecessors have done and his successors will have to do, is how Britain can continue to be a player of global importance when its relative strength is declining. Britain is still the world's fifth or sixth biggest economy, depending upon how you do the sums. She is still a power in world financial markets, a permanent member of the UN Security Council and a nuclear power. She has key seats on the International Monetary Fund and the World Bank.

Set against that, Britain has just one per cent of the world's population and a declining share of the global economy. As China, India, Brazil and other rising powers grow in clout, there will be an ineluctable diminution in Britain's capacity to shape world events, except in concert with other powers.

Tony Blair - and in this, again, he has not been as unlike his predecessors as he may have thought - has tried to have a foreign policy that punched above his country's weight. In some respects, you can say he has been successful. Britain's record in pushing other countries towards agreements on debt relief and climate change is by no means perfect, but it has displayed more energy and commitment than many other world actors.

The Blair doctrine of humanitarian interventionism has not been put into practice in Burma, North Korea or Zimbabwe, as he will regretfully acknowledge. Where Britain could act alone it did in Sierra Leone, where I account it a very good thing to have saved the people of that oppressed corner of West Africa from the sadistic thugs who specialised in hacking the limbs off children. It was a highly creditable act when Tony Blair took considerable risks to lead the case for intervention in Kosovo. Without the pressure he put on Bill Clinton, it is highly unlikely that the Americans would have agreed to threaten Slobodan Milosevic with a ground invasion. Without that threat, the Serbian dictator would have completed the ethnic cleansing of the Kosovars. A side-effect of that intervention became apparent later in the build-up to the war in Iraq and during its searing and grossly mismanaged aftermath. Because he had succeeded in turning around Bill Clinton on Kosovo, it gave Tony Blair an exaggerated sense of his capacity to influence the behaviour of US Presidents.

Another result of this Prime Minister's enthusiasm for a big British presence on the world stage is that she is taking on burdens which others decline to share and which she is now struggling to bear. The most senior British general in Afghanistan has just warned that the country is 'close to anarchy' and that western forces are 'running out of time'. British forces in Afghanistan have already had to be reinforced because the perils of that mission have been terribly under-estimated.

Tony Blair came to power believing that the best way to enhance British global power was through its relations with Europe and the United States. His single most important objective in terms of the EU was to take Britain into the single currency. He failed. Standing outside the euro has not had such bad consequences as Tony Blair once feared. As it turned out, it was the Iraq War that had a much more souring effect on his relations with some key European leaders. Tony Blair found himself doing what every previous British Prime Minister has done, with the partial exception of Ted Heath. Mr Blair has invested most weight on the 'special relationship' with the United States.

History dealt him a tricky hand to play in terms of America. It first gave him Bill Clinton, who was ideologically close, but politically shattered and weakened internationally by his scandal-stained second term. Then the American electoral system produced George Bush, one of the most right-wing Presidents to occupy the White House in decades. The Blair line has always been that unswerving support for the White House in public is the price you pay, however unpopular it might be with the British public, to win private influence. Better, in the Prime Minister's view, that Bush greets him with 'Yo, Blair' than with 'Piss off, Blair'.

It is hard to argue that this has served him well in the eyes of either the rest of the world or his own country. Over Guantanamo Bay, over extraordinary rendition and more recently over the extradition treaty, Britain has ended up looking like an unconditional supporter of - at best as an awkward apologist for - the United States.

When the Lebanon crisis was debated in the Commons, there was an extraordinary unanimity among MPs. They were united, across the parties and ranging from those who had been passionately for the war in Iraq to those who had been as passionately against it. MPs were as one in condemning Hizbollah. They were also universally of the view that Israel's crippling assault on Lebanon is recklessly disproportionate and will prove to be utterly counter-productive. Against this consensus stood the lonely and increasingly battered figure of Margaret Beckett, as the Foreign Secretary stuck with the Prime Minister's refusal to show an inch of difference with America. Britain's position lines her up with the United States against the European Union, the United Nations and nearly all of the rest of world opinion. That is because Tony Blair will never even murmur disagreement with the United States. Especially not when he is going to Washington this week.

You can easily see why he calculated that staying close to America made Britain a bigger player in the world. When this prevents his country having a voice of its own during a crisis as serious as this, the effect of being glued to the United States is to make Britain sound smaller than she is.