The look was one of total surprise. President Trump does not, as a rule, like surprises but he was thrilled by this one.

In addition to the usual official gifts – normally a historic etching or silver dish or handsome bound volume – the King had also packed a hefty chunk of shiny brass aboard the royal flight.

This was the ship's bell from HMS Trump, a Barrow-built T-class submarine which served with distinction in the Pacific in the Second World War. It sank several enemy ships in the Allied campaign against imperial Japan. Mr Trump was so excited that he left his chair at the banquet table to stand alongside the King as he concluded his speech.

'I am delighted to present to you – as a personal gift – the original bell which hung on the conning tower of your valiant namesake,' the monarch stated solemnly. 'May it stand as a testimony to our nations' shared history and shining future.' Then came the wry smile as he added: 'And should you ever need to get hold of us – well, just give us a ring!'

This scene, during Tuesday night's state banquet at the White House, encapsulates why this State Visit has been a resounding success – and it still has plenty of road to run after yesterday's moving events in New York are followed by today's festivities in Virginia.

For the ding-dong moment neatly combines kingly wit, a deftly judged political point, an eloquent reminder of shared heroism, British tradition and precision flattery – all of which have proved to be key elements in managing the current UK/US relationship.

'That is just the sort of thing the President loves,' one of his closest aides told me yesterday. 'We're all going to be sick of the sound of that bell before long.'

The bell idea had not emerged from long committee meetings in Whitehall or Downing Street. It was a brainwave from within the King's own inner circle. Yet it made an important point on behalf of the British government, namely that the Royal Navy – which has come in for repeated jibes from the White House during disagreements over Iran – is a force to be reckoned with.

Or take the King's ostensible congratulations for Mr Trump's upcoming summer of sport. 'In just a few weeks, the United States and Canada will be among those to welcome the world as hosts of the FIFA World Cup. So in one sense, Mr President, as Heads of State, we are joint hosts!' the King joked, adding that he is head of state of five of the competing nations – 'after all, we always like favourable odds'.

Gags aside, here was a clear reminder of Canadian sovereignty to a man who has warned of annexing his neighbour to the north.

The crafty joke technique is working both ways this week. President Trump was also happy to make a less-than-subtle political point. 'We're doing a little Middle East work right now,' he said. 'And we're never going to let that opponent [Iran] ever – Charles agrees with me, even more than I do – we're never going to let that opponent have a nuclear weapon.'

This was clearly a reference to the King's private conversation earlier in the Oval Office and served to suggest that the monarch was more robust on the issue than his lily-livered ministers. One of those who was in the room said that Mr Trump's read-out of the discussion on Iran was rather different from their own. Here was a 'recollections may vary' moment, as the late Queen might have said.

It has also been unusual to hear the King addressed simply as 'Charles' on many occasions. Heads of state are usually sticklers for protocol but the President feels that he now knows the King well enough to drop the etiquette. Nor is he the first president to do this. Nelson Mandela would often address the late Queen as 'Elizabeth' and she never batted an eyelid.

No one on the British side is going to take umbrage at the disclosure of a private chat or first-name terms. The simple reason is that this visit is wreathed in the cosy bonhomie of a royal visit celebrating a 250th birthday.

Americans loved the King's observation that reading a US map is like the family 'Christmas card list across the ages – North and South Carolina, Virginia, Maryland, Charleston (a particular favourite of mine, obviously), Georgetown, Annapolis, and (further favourites) Prince William County and Williamsburg'. Oddly, there was no mention of Sussex County or Henry, West Virginia. Interesting.

Earlier this week, the President had been so pleased by the Mail's revelations of his shared ancestry with the King – both men descend from the 3rd Earl of Lennox (making them 15th cousins) – that he posted my article on his platform Truth Social. As his speeches have made abundantly clear, he is both an avowed Anglophile and a visceral royalist.

At the end of Tuesday's banquet, after the media had left, he made a further short speech off-camera saying: 'It's great to be President but it's nicer to be King.'

All these presidential nods and eulogies to all things British this week may seem bizarre in the face of the administration's derision of Sir Keir Starmer's Government. Just this week, I heard one Trump loyalist, Senator John Kennedy of Louisiana, talking on the Newsmax network where he stated that Keir Starmer was 'as popular in the polls as gonorrhoea'.

Yet these same critics have nothing but the warmest praise and respect for the King and Queen, as has President Trump himself. All week, the Press has waited for him to drop a clanger. Yet it has been the monarch who has delivered one – and very welcome it is, too. Expect to see that bell in the Oval Office very soon.