Tony Blair arrived in the US last night for one of his last official meetings with President Bush. Trips to Washington used to be one of the great privileges of being Prime Minister, an opportunity to exchange the querulous and pettifogging murmuring of Westminster for the dialogue of grand strategy. These days the pilgrimage has become merely a penance.

Washington is not only the author of Mr Blair’s miseries, thanks to the war in Iraq. It is the source of much of the contempt in which the Prime Minister is held in his own country. The man who cast himself as a world leader now looks only demeaned by his proximity to the White House.

The agonies of Mr Blair have revived once again a national debate about that oldest of British obsessions, the special relationship. It is said by Mr Blair’s critics that his subservience to a misbegotten US President has undermined and humiliated Britain, and that his loyalty to the White House has yielded precisely nothing in concrete terms.

Last week, days before Mr Blair was due to set foot on the red carpet, Kendall Myers, a State Department analyst, told a conference that the UK-US alliance was essentially meaningless and that Mr Blair cut a tragic figure. He seemed to confirm the old fear that Americans don’t really take the Brits all that seriously, and that the relationship is no more special than any other.

But it is far too early to pronounce the obsequies on the special relationship. Mr Blair may have blundered terribly in backing Mr Bush over Iraq but the roots of British-American comity are deep enough to survive even this storm.

For starters, it is impossible to read too little into the words of Mr Myers. He is a genial part-time academic who works for the State Department’s Bureau of Intelligence and Research, a widely forgotten and largely ignored part of the vast US foreign policy bureaucracy where the only noise is the occasional sound of axes being ground on the anvils of employees’ resentments.

It is probable that, among serious policymakers in the foreign policy establishment, Kendall Myers is about as familiar as Kendal Mint Cake, and slightly less central to policy discussions.

But, it is asked, as insignificant as he may be, did not Mr Myers merely voice what others with real clout are saying? That the Washington-London axis is a sham, an unequal relationship from which Britain should extract itself? It is perhaps a sign of Britain’s overdeveloped sense of its importance that anyone even queries the idea that the US-British relationship is an unequal one. Given the relative size and weight of the US and the UK, the relationship could hardly be anything other. The US economy is approximately five times the size of the UK’s.

But should not the UK still get something in return for its costly support of the US? Some foreign policy specialists around Mr Blair seem to have deluded themselves that as some sort of payment for Britain’s support in Iraq, the US will agree to lean on Israel a bit harder to make peace with the Palestinians.

The central reality is that no country, by dint of a relationship, special or otherwise, is going to alter policies that it considers to be central to its national interest. There are deep structural reasons for US policy towards Israel and the Middle East that will not be abandoned as a payoff to the British Government.

Does that mean that the UK gets nothing for its unstinting support of the US? Not at all. The US may not change course on the Middle East as a favour to Mr Blair, but there are numerous examples of a disproportionate British influence over US policies that are not central to its national interests.

Ireland is perhaps the most powerful example. The US Government is prey to a wide range of political pressures on Irish policy. Most interested American politicians would have preferred Washington to tilt much more assertively towards the Irish nationalist, or even republican, position over the years. It has not, largely because of the UK’s intense lobbying effort.

The deeper reality is that there is a special relationship. It is measured in the extensive cultural, economic and commercial connections between the two nations. No two large countries in the world are as closely linked as the US and the UK.

The UK remains the largest foreign direct investor in the US. Britons spend more money in America — on business and tourism — than any other nationality. British-American exchanges in literature, cinema, theatre, education and the fine arts dwarf those of any other pair of countries.

The special relationship is more to do with the common values and interests than with the imprecise calculations of geopolitics. It will survive a botched war or two.

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