When Bill Clinton left the White House in January 2001, he was replaced by the conservative Texas Republican George W Bush. As Mr Bush was inaugurated, I asked an American policy adviser for advice: the British government of Tony Blair had been very close to Mr Clinton, so how should Mr Blair deal with Mr Bush’s very different administration?
The response was that Mr Bush and Mr Blair inevitably would work together well, but Mr Blair should get as close as possible to Mr Bush, despite their very different ideological mindsets. Perhaps Mr Blair received similar advice from his own advisers.
Certainly by the 2003 invasion of Iraq, the two politicians moved in lockstep. Mr Blair had some influence in persuading Mr Bush to work within the UN. Mr Bush had Mr Blair – and the British military forces – as allies for the overthrow of Iraqi dictator Saddam Hussein.
As another US diplomat once said to me, “when we say multilateral, we mean 'get the Brits on board'". For “the Brits”, that has often meant talking up a “special relationship” with the US. Since the Second World War, a central ambition of British diplomacy has been to act as a bridge between the US and its European allies.
The UK-US relationship was seriously tested during the Trump presidency. The former UK ambassador in Washington during the Obama years, Peter Westmacott, has been discussing the ups and downs in his new book, They Call It Diplomacy. Mr Westmacott had 40 years representing Britain abroad. He is scathing about the Trump administration but also revealing about the UK's strategic weakness. As he puts it: "Britain's first instinct, especially when it does not know what to do, is to ask the Americans, but that was near impossible when US policy was being made by early-hour tweet."
Donald Trump's undiplomatic Twitter diplomacy was made worse by the fact that he did not think much of his own American experts, the career diplomats in the US State Department. He didn't fill key posts, and he couldn't retain talent in key positions.
In policy terms, there was plenty of hollow talk about the possibility of a rapid UK-US trade deal after Brexit. Such agreements are complex treaties that take years to negotiate and ultimately have to pass through the US Congress.
When Mr Westmacott's successor as British ambassador, Kim Darroch, suggested in private emails to London that the Trump administration was dysfunctional, you might think this was hardly "Top Secret". But when the emails were leaked, Mr Trump had one of his fits of pique and made clear that Mr Darroch should go. The British foreign secretary at the time was Boris Johnson, who supinely refused to back Mr Darroch for stating what was utterly obvious. Mr Darroch had to resign – a sad moment when a diplomat with an impeccable record loses his job for the crime of telling the truth in confidential cables to his own government.
All this is just background to the obvious fact that the US-UK relationship is very close but also very unequal.
A new generation of British diplomats must now reset relations once more to make sense of a new – but more predictable – US administration. Joe Biden promises great change and has begun delivering. The Biden reset means that the US is back in the game of seeking international co-operation, playing a prominent and often leadership role in international bodies including Nato, the WHO, and on climate change.
"America is back; diplomacy is back," Mr Biden told State Department staff in a morale-raising visit. He has spoken to friendly world leaders "to begin re-forming the habits of co-operation and rebuilding the muscles of democratic alliances that have atrophied over the past few years of neglect and abuse".
Some world leaders, seen as close to Mr Trump, were not high on Mr Biden's list for a chat, including Israel and Turkey. Mr Biden has withdrawn support for the war in Yemen. He has cancelled Mr Trump's order to pull 12,000 troops out of Germany. There has a been a difficult phone call with Vladimir Putin and the US relationship with China – and Taiwan – is about to enter a new phase, too, although the next steps are unclear.
In London, meanwhile, there is excitable talk in government circles about a post-Brexit "Global Britain". But it is without any clear meaning beyond the Trade Secretary enthusing about a possible trade pact with Pacific nations. Pulling out of the European Single Market while pushing for a Pacific trade deal seems a bit odd for the British isles, which, geography suggests, are fated to remain on the other side of the world in the Atlantic. Moreover, that old idea of an American president ever having to call Europe by going through a British switchboard is as antiquated as the telephone technology of the 1950s and 60s.
However, there are grounds for optimism. British diplomats – the skilled successors to Mr Westmacott and Mr Darroch – have equally skilled American counterparts now to work with. And, at least, diplomats from all countries no longer have to worry that a 5am tweet from a listless president will wreck all their careful conversations.
Gavin Esler is a broadcaster and UK columnist for The National