Who would have thought it? There is nothing in President Obama's background to suggest that he would have bonded so easily with a British Conservative Prime Minister. When Mr Obama was elected, the Europhile bien-pensants who have had such a poisonous influence on British foreign policy in recent decades thought that they saw an opportunity to undermine trans-atlantic links. As usual, they were mistaken. They have been as hostile to the special relationship as the Vichyites were to de Gaulle. Somehow, it has survived.

But there have always been problems. Churchill and Roosevelt coincided in their love of grandeur and they had a war to win. Despite that, their personal relations were never wholly harmonious. Thatcher and Reagan: ideological comrades, and he radiated chivalry towards her. When the great ones break for lunch at G8 meetings et al, the placement is normally head of government, foreign minister, head of government – and so on. Mr Reagan would always switch his card so that he got to sit next to Margaret. Yet that most sentimental of eras in the special relationship did not prevent some awkward moments in the early phases of the Falklands War.

Apropos of Reagan and Thatcher, there was once a glorious tease. From time to time, Ted Heath would have lunch parties at his house in the Close at Salisbury Cathedral. On occasion, he was sullen and sulky and porcine. Those were the good days. On one of the bad days, the guests included Ray Seitz, the then American Ambassador. Ted was at his worst: the platonic idea of gracelessness. Finally, Ray could stand it no longer. "Ted, you've seen a fair few Presidents and Prime Ministers. Which of them had the best working relationship?" The reply was as inevitable as it was dishonest. "Nixon and I, of course". "And after that?" " Oh, Harold Macmillan and JFK". "But aren't there any more recent examples, perhaps from the 1980s?" The old swine squirmed. "I don't know what you mean".

Although John Major and George Bush senior always got on well, the most successful period in the post-war special relationship was also the least predictable: Tony Blair and George Bush minor. It did help that Mr Blair converted to neo-Conservatism. But that unpredictable second baptism should not obscure a more general lesson. Being in a relationship with the US is like going to bed with an elephant. Whatever the pachyderm's protestations of affection, it will hog the bed-clothes. The more the UK agrees with the US, the more easily the special relationship will work. The agreement was never closer than under Bush/Blair.

Even so, we British can take a certain cautious satisfaction from the past couple of days. In the first place, we have a wholly presentable Prime Minister. He does the country proud – and Sam is not bad either. You are a politician with an election to win. Which foreign leader would be most useful? Mr Obama would probably still top the poll, though by nothing like the same margin as in 2009. But anywhere outside France, David Cameron would come second. The French can be left to stew in their irrelevant and inspissated resentments. Today, they would prefer Angela Merkel.  In 1940, they would have preferred Adolf Hitler.

There is a further point, which goes deeper than glamour. The world has rarely appeared more uncertain. There are vast questions which affect all our futures. Mishandled, they could lead to catastrophe. But there are no obvious answers. The future of the Middle East, of Russia, of China, of the Eurozone: in each case, no-one knows. Geo-poltical uncertainty will be reinforced by crises over energy and water. Yet in all the clouds of doubt and danger, there is one consolation. Britain is in a strong position to take part in the debates. We have historic expertise; we have always been good at thinking about foreign policy. We are often in the centre of the concentric circles, and every recent American President has concluded that we are a vital ally.

As for the special relationship, there is an obvious conclusion. It has never been as harmonious as the illusions of British naivete would have wished to pretend. It has merely been indispensable. So it will remain.