With the approach of a prime ministerial visit, the Ambassador's pulse quickens. Apart from a visit by the Sovereign herself, not much pumps the adrenalin faster for the British Ambassador in Washington. When it is the first official visit to a new President, it can be a career-defining moment. You are responsible for making the visit a “success”. If it is, No10 will take the credit and the most you can do is to bask in reflected glory. If it is a failure, the can is all yours to carry.

Success means that Prime Minister and President get on well and largely see eye to eye on the big issues. But even more important to the No 10 machine is that the visit be seen as a success by the media. If it is true that Gordon Brown hopes to catch a little Obama stardust to alleviate his domestic political woes, the press conference at the end of the visit will assume extraordinary significance. Reporters, especially the British, will parse every word, scrutinise minutely every twitch of body language, to reach a judgment on the health of the “special relationship”.

In 2001, after a successful first meeting between Tony Blair and GeorgeW. Bush, the press conference went off-message with the President's bizarre reference to using the same toothpaste as Mr Blair, in answer to a question about what they had in common. It required frantic remedial action to explain that the cabins at Camp David were equipped with Colgate toothpaste - and that this was Mr Bush's wacky sense of humour. Two years later, just before the Iraq war, the demeanour and words of Mr Blair and Mr Bush at a White House press conference vividly revealed the tensions of the moment.

By now, our Ambassador in Washington, the able Sir Nigel Sheinwald, will have done just about everything he can to ensure success. He will have warned No 10 of any bear traps lurking in Washington, set out what the Americans want, recommended what Britain should try to get, given advice on how to handle Mr Obama and offered an assessment of his Administration. Sir Nigel, in daily contact with the White House, will bring Mr Brown up to date as they travel from the airport in the embassy Rolls-Royce (or is it a Bentley these days?).

The Americans too will want the visit to be seen as a success. On past form, both sides will be near agreement on what Mr Obama and Mr Brown will be able to say in public. Little is left to chance and the degree of unscripted negotiation on the day is highly limited. Quite possibly a draft statement already exists, setting out the issues discussed and decisions reached. The top subjects appear to be the economic crisis and Afghanistan: these will be at the hard centre of what Mr Brown grandiosely calls a “global new deal” to be struck with Mr Obama. He will seek to cloak himself in Mr Obama's mantle and show that Prime Minister and President are as one as they go into April's G20 meeting in London. On Afghanistan, understanding will have to be reached on how many more troops we are prepared to commit. This will surely require agreement on the strategic purpose of our joint intervention, something that, even after eight years, is still unclear.

Sir Nigel has done well to get Mr Brown to Washington before other European leaders, even better to have secured for him an address to a joint session of Congress. It took Mr Blair eight years to be accorded a similar ceremony in 2005. Labour/Democrat connections may have played a role. Mr Brown has longstanding contacts with the Democrats from Bill Clinton's time. We are told that No10 is cock-a-hoop and President Sarkozy mortified. Officially, No 10, the Élysée and the Kanzleramt affect indifference about who gets to see the new president first. But in private it is another matter. It was made plain to me in 2000 that Mr Blair wanted to be the first foreign leader to pay an official visit on Mr Bush. I managed to contrive this after President Fox of Mexico, with whom, the White House pointed out, Mr Bush shared a common frontier and a love of ranches and cowboy boots.

At first blush, it is surprising that the Americans are pushing the boat out so far for Mr Brown. They must know that the next prime minister may well be David Cameron. Is this an attempt to affect the course of British politics in Mr Brown's favour? I doubt it. We should not exaggerate the significance of these American marks of respect. For some months there has been a testiness in Anglo- American relations, especially over Iraq and Afghanistan. Rendition and Guantánamo have been a drag on the relationship. It is not in America's interest for Britain to be estranged, especially as we will remain the second-largest troop contributor in Afghanistan.

Washington knows that, above all, Mr Brown wants to bathe in the approbation of President Obama. So, a gesture here, a gesture there will keep us sweet: our tummies will be tickled with frequent invocation of the “special relationship”. But, the Americans must doubt, as do I, that any amount of Obama stardust will affect Britain's next general election.

Let's hope, for Britain's national interest, that this visit is a substantive, not just a presentational, success. America remains our single most important partner and ally.

But let's keep our heads. Even if the “special relationship” is declared alive and well, it does not necessarily mean that we shall be more important to the US than France or Germany, as Mr Brown seems to be suggesting; or that, where our interests diverge, we should not fight our corner with all possible vigour, as the Americans will certainly do.

Sir Christopher Meyer was the British Ambassador to Washington 1997-2003

Times Recommends

• The ghost of Robin Cook haunts Chilcot’s feast
• The truth shouldn’t need oaths
• Violence: let’s separate the men from the boys