Seldom has a US presidential election campaign been watched from the opposite side of the Atlantic with so much grim fascination and nervous anticipation as the present contest between George W. Bush and John Kerry.

Seldom, too, have Europeans been quite so partisan in their support for one candidate. In one opinion poll after another, it is clear that Mr Kerry is Europe’s overwhelming favourite. In Germany, nearly 80 per cent of the electorate prefer the Democratic contender to Mr Bush. In France, only 5 percent back the incumbent. Even in the UK, where Tony Blair has been such a loyal ally, the margin is 47 per cent to 16 per cent in favour of Mr Bush’s challenger, according to a recent GlobeScan poll.

“There is this very widespread sense that anything that will punish Bush is good for humanity,” says Francois Heisbourg, director of the Foundation for Strategic Research in Paris. “That keeps the interest alive.”

A senior British official in Brussels says: “We have to face the fact that in Europe, Bush is not a brand that travels well.”

The reasons concern both substance and style. “We would like to have a president who not only says he believes in effective multilateralism, but who really acts like that,” says Gert Weisskirchen, foreign policy spokesman in the German Bundestag for the ruling Social Democratic party (SPD).

According to a European ambassador in London, dislike of Mr Bush stems partly from Europeans’ hostility to his ideology. “It is a very rightwing ideology in social matters that is not shared in Europe.” Europeans also perceive a “mix of nationalism, arrogance and unilateralism”, he says. “These people do not care about what the rest of the world thinks. That is an element peculiar to the Bush administration.”

But Europeans do not have a vote in the US elections. They are also increasingly aware that their preferences are not shared by the US electorate.

They see that Mr Bush is once again leading in many US opinion polls.

Indeed,the fact that countries such as Germany and France are hostile to the president may even count in his favour among US voters.

In the corridors of power in Berlin, London, Paris and Rome there is a more nuanced view about what sort of US administration would actually be good for Europe.

Part of this analysis is a feeling that relations could scarcely get worse than they have been with the Bush administration, while there would be a real danger of exaggerated expectations from a victory for Mr Kerry. “If Mr Bush wins again, we will both start with thoroughly low expectations of eac other,” says a seasoned European Commission diplomat. “That is not a bad place to begin from.

As for Mr Kerry, expectations would be much higher, and therefore there would be a danger of disappointment.”

An immediate concern relates to the war in Iraq, and the fear that Mr Kerry would expect a greater European contribution in both troops and money. “If the reconciliation that he offers means the policy in Iraq will be different in style but not in purpose, that could lead to misunderstanding,” says a top French diplomat. Michel Barnier, the French foreign minister, flatly ruled out sending French soldiers when he spoke at the UN last week. “That was a message for Mr Kerry more than Mr Bush,” the diplomat said. Gerhard Schroder, the German chancellor, is equally determined to resist sending German troops.

The more fundamental European concern, however, relates to the awareness that transatlantic relations are passing through a traumatic period that goes well beyond the disaffection with the present Bush administration. It is a change that really dates from 1989, with the fall of the Berlin Wall.

And it coincides with a growing divide on social and cultural values.

“This trend was not invented by Mr Bush,” says another senior French ambassador. “It existed before because of the end of the cold war and the disappearance of any counterweight to US power in the world. Europe as a whole was devalued strategically in American eyes.”

The change in strategic perception was blurred in the 1990s because of the Balkan wars, when the US had to help Europe in Bosnia and in Kosovo. “When that was over, and 9/11 happened, Europe became secondary again in American eyes,” the same French ambassador says. “I do not think that would be very different for a President Kerry. Of course we have a strong link, and many shared values.

But the world we live in is not the same. America has changed, and Europe has changed too.”

The depth of the transatlantic divide has been exposed in a series of opinion surveys, including the German Marshall Fund’s annual Transatlantic Trends report. IT shows a drift apart not so much in basic values, such as a belief in democracy and the market economy, but in reactions to common threats, support for the use of military force, and in more subtle social values.

“Something fundamental is happening in transatlantic relations,” says Ulrike Guerot, Berlin-based transatlantic fellow with the GMF. “There is something of a systemic rupture.”

The latest GMF survey showed that Europeans and Americans share much the same view of current threats: international terror and Islamic fundamentalism come top, although weapons of mass destruction are feared more by Americans than Europeans. It is on the use of force to tackle those threats that the divide emerges, and over the use of the United Nations and the multilateral system (see charts below).

“Europeans are much less willing to use force to maintain peace or obtain justice, and they are broadly unwilling to use force without multilateral approval,” the GMF reported this month. “The transatlantic split on these issues is substantial, but so are the divisions within the US and Europe.”

The war in Iraq, and the Bush administration’s commitment to pre-emptive military action to tackle terrorist threats, have brought those differences to a head. Although Europe split on Iraq, the division is becoming narrower and less bitter. Not only has Spain pulled out of the US-led coalition in Iraq, but others such as Poland are getting increasingly nervous.

Some European observers believe a second Bush term would actually help re-unite Europe. “We’re going to have a paradox,” says Mr Heisbourg. “If Bush comes back, the ‘old Europe-new Europe’ divide will continue to heal. Both new Europeans and old Europeans have realised this was incredibly damaging for the EU.”

Iraq would be one test. Iran would be another. “The Bush camp is so divided on Iran they have not been able to devise a joint strategy with us,” says the senior French diplomat. “It should include clearer sticks on the European side, and clearer carrots from the Americans. But Bush is torn between the hardliners who will only settle for regime change and those who live in the real world. I think Kerry probably has more room for manoeuvre.”

Some Europeans, particularly in London, argue that a second Bush administration would be very different from the first, just as the second Reagan administration was far more sensitive to international diplomacy than the first.

It is not a widely held view elsewhere on the continent.

“I do not believe that (Bush) will become more like a traditional internationalist Republican,” says Marta Dassu`, director of policy programmes at the Aspen Institute Italia. “Either he decides to go back to the semi-isolationist mood of 2000, combined with strikes for security reasons, or he goes on opening new diplomatic problems, such as Iran.”

Another test will be the Arab-Israeli peace process. All European governments, the UK included, have been disappointed with the failure of Mr Bush to put his heart into the “road map” for peace, and apply serious pressure to the Israeli government to stop building settlements on the West Bank. But they are not holding out much hope for a big change with a Kerry victory.

One key part of the relationship that could see a very different tone regards Nato. The GMF survey showed that Democrats are much more enthusiastic than Republicans about keeping the old alliance in good shape.

Europeans in Nato have never recovered from the insistence of Donald Rumsfeld, the US defence secretary, that “the mission determines the coalition”. It undermined the entire concept of a permanent alliance.

Yet there is nervousness even there that Mr Kerry might regard Nato as an easy way of being multilateral while still failing to heed allies’ doubts. “The Democrats are not as keenly aware as the Republicans how much the alliance has dissipated,” says Mr Heisbourg. “They will try to revive it, not kill it.

But Nato looks increasingly like an American-led organisation to provide European troops for American purposes. That is not a winning proposition.”

Seasoned European observers of the US caution against two things: assuming election campaigns reveal future foreign policy; and expecting a second administration to be the same as the first. Yet they are still very nervous.

Chris Patten, the European commissioner for external affairs and a staunch Atlanticist, finds the rhetoric at the Republican convention in New York “unsettling”.

“If you want to get a cheap cheer from certain quarters in America, it seems that all you have to do is bash the UN, or the French, or the very idea that allies are entitled to have their own opinions,” he told the European parliament two weeks ago. “What I most worry about is that on either side of the Atlantic we will bring out the worst in our traditional partners. The world deserves better than testosterone on one side and superciliousness on the other.”

If Mr Kerry were to defeat Mr Bush on November 2 most Europeans expect more of a change in style than in substance. But in international diplomacy style matters a great deal. If Mr Bush wins again, few expect to see much easing of transatlantic tensions.

Whatever private thoughts he may harbour about the forthcoming US presidential election, Tony Blair has always refused to make them public. Asked on television yesterday what he thought about the prospects for George W. Bush and John Kerry, the prime minister’s response was as tight-lipped as ever: “I’ve got enough to worry about with my politics without worrying about theirs.”

But nobody doubts that the outcome of the US election will have significant consequences for the prime minister and for British politics. If Mr Bush were re-elected it would raise further questions in Britain about whether Mr Blair would be prepared to back Washington’s neo-conservative foreign policy. The election of John Kerry, while it would prove initially highly embarrassing for the prime minister, might make life easier for Mr Blair in the run-up to the general election expected next May.

Mr Bush’s re-election this November would be of some immediate benefit to Mr Blair. The prime minister is Mr Bush’s closest international ally and a strong voice in Washington.

But in the longer run, Mr Bush’s return to the White House would put Mr Blair under renewed pressure. The prime minister has come under attack both within his own Labour party and across the country for his stance on Iraq and for the failure to find weapons of mass destruction. Labour supporters’ disillusionment with the prime minister’s Iraq policy is so great that Labour is set to lose some 3m votes at the next general election, according to the party’s private polling.

The re-election of a Bush administration could therefore once more expose Mr Blair to conflicting pressures in the field of foreign policy, especially with regard to Iran. According to some Whitehall insiders, Mr Blair would be ready to back any call by Mr Bush for tough action against Iran if diplomacy failed to curb Tehran’s nuclear programme. But after the Iraq debacle, Mr Blair would not have the political capital for such pre-emptive action.

Tensions with Mr Bush could also arise over the Middle East peace process.

“Tony is convinced that a second-term Bush will change his stance and put more pressure on Israel to sue for peace,” says one leading Labour figure. “His calculation is that Bush won’t owe anything to anybody any more, and can therefore put pressure on Israel.” But if US policy on the Middle East remains the same, the prime minister will once more be in a quandary – forced either to back Mr Bush or break with him.

A win for John Kerry would create a different prospect. In the immediate aftermath of a Kerry victory, Mr Blair would be the clear loser: a man who backed a one-term president and ended up on the wrong side of history, like Jose Maria Aznar, Spain’s former prime minister, who supported war in Iraq and was defeated in an election this year.

“The headline will be two down – Aznar and Bush – and one to go – Blair,” said one cabinet minister yesterday.

But the benefits to Mr Blair of a Kerry victory could be significant in the long run. Mr Kerry’s policy on Iraq would be no different from the Bush administration’s, say UK diplomats. But Mr Kerry is considered likely to take far more concerted steps than Mr Bush to tackle the Israeli-Palestinian problem. He would also be likely to restore greater respect for multilateralism to US policy, engaging more deeply than Mr Bush with France, Germany and the European Union.

If Mr Bush wins, the agony of being a bridge between a unilateralist US and a discontented Europe can only get greater for Mr Blair.

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