So much for all those prim demands that the King's state visit be cancelled for fear that Donald Trump would somehow 'embarrass' the King.

If there was any embarrassment yesterday, it stemmed from a host voicing such exuberant praise for his guests – and obvious delight at their presence – that any self-respecting old-school Brit would have turned deepest red.

Americans owe their very existence, the President declared in his speech of welcome, to 'the ancient English love of liberty' and 'Britain's distinctive sense of glory, destiny, and pride'. The US's revolutionary founding fathers were blessed with 'the rarest of gifts – moral courage – and it came from a small but mighty kingdom from across the sea'.

As for the Royal Family, President Trump reminded us that his beloved mother had worshipped the late Queen all her life while describing the young Prince Charles as 'cute'. 'My mother had a crush on him – can you believe it?'

To which one might well respond: can you believe that this was the very same Donald Trump who, in recent weeks, has painted Britain and its politicians as craven, feeble, ungrateful losers – while mocking our Royal Navy? Indeed it was.

Standing on the South Lawn of the White House, in front of the largest guard of honour ever assembled for a state visitor, the President was clearly set on channelling his inner Winston Churchill as he welcomed the King and Queen.

Here was a display of brazen, unabashed Anglophilia of a sort we would never have heard from Mr Trump's predecessor, Joe Biden. This was a comprehensive eulogy to the British DNA running through the veins of the USA. Mr Trump even used the 'S' word – cheerfully proclaiming the 'special relationship', the phrase studiously avoided by the Foreign Office.

What yesterday reminded us very clearly is that there are two transatlantic relationships and they operate at very different levels. The one between the White House and Downing Street is a fragile one right now. The one between Pennsylvania Avenue and Buckingham Palace, however, is just fine and dandy. That was the one on show yesterday. Even the rain felt British – as the President joked at the start of his speech.

It was yesterday's Daily Mail which had set the tone. The President's first public utterance of the day came yesterday morning when he posted my article about his ancestry to his millions of followers on social media.

I had reported that Mr Trump and the King had a common ancestor in the 16th century, the 3rd Earl of Lennox, from whom both men are directly descended.

One of the Earl's sons went on to produce a direct line through the Stuarts and Georgians down to the House of Windsor. Thanks to his daughter, another direct line passes down through three clans – the Gordons, the Mackays and Macleods – to Mr Trump's mother, Mary Anne Macleod, who subsequently moved from Scotland to the US and married Fred Trump. The King and the President are thus 15th cousins.

This had clearly put him in a very good mood. 'Wow, that's nice,' he wrote on the Truth Social platform, above a copy of my article. 'I've always wanted to live in Buckingham Palace!!! I'll talk to the King and Queen about this in a few minutes!!! President DJT'.

Moments later, more than 500 members from every strand of the US armed forces started lining up on the White House lawn. We had been told to expect 'opening remarks' from Mr Trump but this was a full-throated exaltation, saluting Britain's legacy from Magna Carta through to the Declaration of Independence to the present day.

Then it got personal as he reflected on 'Her Late Majesty, Queen Elizabeth, an incredible woman who I had the privilege of getting to know… very greatly missed on both sides of that mighty Atlantic'. He spoke of the tree she had planted in the grounds, now standing tall, and applied the same analogy of deep roots to both the US and his own kith and kin.

'It reminds us that the mightiest of trees, like the greatest of nations, must be anchored by the strongest and deepest of roots. Americans have had no closer friends than the British.'

He turned to his own 'wonderful mother', born in Stornoway on the Isle of Lewis. 'That's what they call very serious Scotland,' he noted proudly.

He told how his mother had left for the US, met her husband and enjoyed 63 years of marriage. He then turned to Melania (the third Mrs Trump) and joked: 'That's a record we won't be able to match.' The First Lady's trademark steely poise broke into a glint of a smile.

Not only was Prince Charles 'cute' as a boy, but he was about to be the first British King to address a joint session of Congress (the only previous monarch having been the late Queen in 1991). A few hours later there was much the same warmth as the King was welcomed into the Chamber of Congress.

No one looked more relieved yesterday than the British Foreign Secretary, Yvette Cooper. For a few days – at least – the relationship is going to be as 'special' as it has ever been. That will doubtless change. But the UK might as well enjoy it while it lasts.