Tony Blair used to say that the British voters wanted him to have a Love Actually moment - and tell the President of the United States to get lost, as the Prime Minister played by Hugh Grant does in the film. As Barack Obama prepares to move into the White House, Gordon Brown is more likely to find himself in a Mamma Mia! situation. He is one of several people competing to be the political equivalent of the father of the bride.

Along with Nicolas Sarkozy (Piers Brosnan) and Angela Merkel (Colin Firth) the Prime Minister is begging the most popular man on the planet: take a chance on me. In his new year message, he promised to spend money money money on an economic “coalition for change” with Mr Obama. Now he is racing to be the first leader to visit the president in Washington; to the tune I Have a Dream, he is preparing to woo Barack with policy papers at the G20 summit in London this April.

Like Meryl Streep's former lovers on the Greek island, however, Mr Brown will end up having to share Mr Obama. The inauguration of a president who is adored by the British public could ironically spell the end of the special relationship between the UK and the US. Just as the voters in this country decide that it is time to get up close and personal with America, so the Yanks are losing their passion for the Brits. Just as the Prime Minister decides it is time to stand shoulder to shoulder with the US president, so he may find the cold shoulder turned on him.

This is partly but not entirely about Mr Obama. Certainly, the President-elect will be the least Anglophile American leader in living memory. Unlike Bill Clinton, who was educated at Oxford, or George Bush, who kept a bust of Winston Churchill in the Oval Office, Mr Obama has no innate affection for this country - in fact, his grandfather was imprisoned and tortured by British colonialists in Kenya.

When he was looking for a symbolic place from which to address Europe - and the world - he chose not Trafalgar Square but the Brandenburg Gate. It was a deliberate attempt to distance himself from the Bush Administration - by going straight to the heart of what Donald Rumsfeld once called “old Europe”. If he wants to prove his ability to build new alliances, he will not start in this country. “The UK is part of the Bush baggage because of Iraq,” says a senior Foreign Office source. “Obama is not going to be emotional about the transatlantic alliance. He's a free-thinking politician, driven by science and facts. The UK and Europe look less significant than Asia and Latin America and even over here Europe seems a better focus than the UK.”

The British position has not been helped by Sir Nigel Sheinwald, the Ambassador to Washington, a career diplomat educated at Oxford, whose pin-striped demeanour does not fit easily with the open-necked attitude of the Obama camp. A memo, leaked last year, in which our man in DC described the President-elect as “aloof”, “insensitive” and lacking a track record did not go down well with a politician who already suspected the British of having a superiority complex.

There will, of course, be common ground between Mr Brown and Mr Obama on the recession - both men are strong advocates of a global fiscal stimulus. But the Prime Minister's vision of himself as sage adviser, offering a helping hand to the youthful novice, is likely to end up as the audacity of hope. The President-elect's maxim about the challenges being big, but politics being small (which Mr Brown likes to quote) can be transposed on to the transatlantic relationship: rarely has politics in this country seemed so tiny, compared with what is going on in the United States.

Perhaps most important of all, the military alliance between Britain and America - which has cemented the political alliance since the First World War - is beginning to crack. I am told that a report circulating at the highest level in the Ministry of Defence concludes that there are now serious doubts in Washington about the effectiveness of the British Armed Forces. Senior military figures are said to have been surprised, and shocked, by feedback that arrived in Whitehall last month. Described as “highly sensitive”, it raised questions about the worth of the UK contribution to US-led operations in Iraq and Afghanistan. “It showed that the Americans don't value us much,” one source told me. “Britain's military ability is no longer rated as highly as we thought it was.”

This is not a last gasp by the outgoing Bush administration. Robert Gates, the US Defence Secretary, who has been asked to remain in his job by Mr Obama, is one of those said to have reservations about the British military contribution.

The message has filtered across to the Foreign Office, too. At a diplomatic as well as a military level, concerns have been raised about the quality of British troops and equipment. Too often, the Americans complain, they have had to ride to the rescue of the Brits, rather than being able to rely on them as equal partners. There are question marks in Washington about Britain's political commitment to military engagement: Mr Brown will not be forgiven if he fails to send substantial numbers of troops to support an Obama surge in Afghanistan.

“The US generals think the Brits need to be taken down a peg or two - that we have not performed well in Basra and Helmand province - and that has trickled up to the Pentagon,” says a Foreign Office insider. “It's not terminal but it's an important warning to us that if we are going to trade on our military partnership we are going to have to raise our game.”

Mr Obama won power promising change. Mr Brown wants nothing more than to bask in the reflected glory of that. But it looks as if the Anglo-American alliance will be one of the first targets for change. One minister says the “specialness” in the special relationship will be diluted. It may not survive at all.

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