What will the Queen and Donald Trump discuss over tea during his state visit?

The heroic inscrutability that has defined Queen Elizabeth II since she ascended to the throne in 1952 faces a rigorous new challenge. Donald Trump is to make a state visit next summer, and if anything seems calculated to explore the outer limits of her sangfroid, this is it.

As any Netflix subscriber who has binged on The Crown will understand, being sovereign is not an easy job. It brings not only a level of relentless tedium that would break a coma victim in weeks, but the demand to mingle with some of the species’ least savoury creatures at the Government’s behest.

In her almost 65 years on the throne, to pluck a few horrors from so many, Her Britannic Majesty has had Bashar al-Assad over for tea, shared a horse-drawn carriage with Nicolae Ceausescu and dabbed the shoulders of Sir Jimmy Savile and Robert Mugabe with her sword.

No one is better at masking boredom and being blandly pleasant to the grotesque. Yet has anything adequately prepared her for having President Donald J Trump to stay at Windsor Castle, and hosting a state banquet in his honour?

In an episode of The Crown, very early in her reign when President Eisenhower is scheduled for such a visit, the Queen is so worried about her lack of education that she hires a tutor to prep her for the meeting. Eisenhower’s big thing, he tells her, is the danger to peace posed by the military-industrial complex. She frowns. That, adds the tutor, and golf. She frowns harder.

Even if Trump didn’t love the poorly educated, she’d have no cause to fret about her ignorance with him. The Queen has learned more than enough about geopolitics over almost 65 years for a guest whose ritalin-defying attention span suggests he’ll know nothing more after six months in the Oval Office than he does today. Which is nothing.

In that case, she will need to find other conversational common ground. One possibility is Princess Diana. Trump told Howard Stern, soon after she died, that although Diana was “crazy”, he could have had sex with her. The Queen might privately agree with the first bit. But you can’t imagine her saying so, let alone engaging with Trump about the second bit.

So far as sport, we can rule out golfing chit-chat on the Eisenhower precedent, while Trump’s interest in thoroughbred racehorses presumably begins and ends with fantasising about placing their severed heads on business rivals’ pillows.

Children are a useful gambit in uneasy social situations, so I offer the 45th President this ice-breaker if things tend toward the silent over the soup. “You know, Ma’am, that we both have three sons and a daughter!” “We were under the impression, Mr President, that you have two daughters.” “Nope, just Ivanka.” “And what of Tiffany?” “Oh yeah, Marla’s kid. Always forget Tiffany.”

Were she less puritanically averse to taking the easy option, she would dump Trump on Prince Philip and ignore him entirely. Politically incorrect soulmates, The Donald and the Duke could indulge in a riot of mutual admiration. “Hey, I loved it when you went to China and told that English kid he’d get ‘slitty eyes’ if he stayed.” “And I was most impressed, Mr President, with your thoughts about the people of Mexico.”

The expectation that those two would get on like a house on fire seamlessly brings us to the strongest bond between Queen and President: each owns a dazzling amount of prime real estate.

Even if Trump finds the decor a touch understated for his taste, he could use Windsor Castle to plug a conversational hole.“That fire you had here back in ’92,” as a scene in series 12 of The Crown might relate, “Insurance job?” “Good grief, no, Mr President, a dreadful accident. My annus horribilis.” “Look, I have the most tremendous proctologists next time you’re in the States...”

Meanwhile, in homage to his one area of real expertise, the Queen could pick Trump’s brains about refurbishing her London home. If she agreed to it being restyled “Trump Buckingham Palace”, on the lines of the sadly defunct Trump Taj Mahal in Atlantic City, only more blingy, he might even pay the £369m for the work himself.

So there is hope that the encounter between humanity’s most reticent woman and its most verbally incontinent man will be less excruciating than decency demands. And perhaps the Government’s cunning plan to use her star power to bypass Nigel Farage and finagle Trump into making a quick and a deal favourable with Brexit Britain will work.

But spare a thought for the monarch as she contemplates the arc of queenly-presidential relations. As a very young queen, her first President was Eisenhower, the scandal-free former general who avoided wars and became an emblem of the empire at its most benign. With her turning 91 next year, there is a fair chance that her last will be a draft-dodging vulgarian whose bellicose buffoonery must be fancied to bring the American empire to its knees.

She will her do her duty with the usual stoical detachment, sitting up and thinking of England, and giving no hint of any personal distaste. But somehow it’s comforting to imagine Her Maj being as revolted by the requirement to suck up to President Trump as anyone else.