We all know about Franklin and Winston, Ronnie and Maggie, and George and Tony. For better or worse, these transatlantic allies enjoyed grand visions, global power and left indelible marks on history. But now we have Donald and Boris, whose grand visions stare back at them each morning in the mirror.

Quick Guide Boris Johnson's to-do list Show A cabinet reshuffle The first task of any new PM involves rewarding some loyal allies and disappointing more. Several Johnson loyalists have had their eye on the post of chancellor, but only one can do it. A complete clearout of May’s remain-minded ministers provided plenty of opportunity to reward the Brexit believers though. Brexit The issue that will define a Johnson premiership. He has promised to rapidly renegotiate almost all of May’s departure deal, ditching the Irish backstop border guarantee policy – something that would seem a huge task over any timescale, let alone little more than 12 weeks, a fair proportion of which is taken up by a summer break. If this fails, he will be set on a no-deal departure for 31 October, and a likely huge clash with MPs. Iran If Brexit wasn’t enough, a new Johnson government must immediately take steps to make sure he doesn’t begin his time in No 10 with a slide into war. The situation in the gulf is complex, fast-moving and hugely dangerous. Johnson did not cover himself in glory as foreign secretary, especially over Iran. It will be his task to prove he has learned. Managing parliament and Tory MPs Johnson will start as PM with a working Commons majority of four, thanks to the DUP, but within weeks it is likely to be down to three if as expected the Liberal Democrats win in the Brecon and Radnorshire byelection. If this wasn’t tricky enough, a small but significant section of Tory MPs openly detest Johnson, and will not want to help him out - and with his cabinet sackings, the ‘Gaukward squad’ of former senior cabinet members set on blocking a no-deal Brexit swelled in ranks. Loosening the purse strings Such was the fiscal largesse on display from both Johnson and Jeremy Hunt during the hustings process that much as he will seek to kick any decisions towards an autumn budget, voters – especially Tory members – will be expecting both tax cuts and more spending on areas such as education and the police. Everything non-Brexit This might sound glib, but there is a lot to consider – during the three-plus years of Brexit introversion May’s government failed to properly grasp any of a series of long-term, pressing national problems: the crisis in social care; the future of the NHS; a climate emergency; the increasingly insecure future of work; a broken housing market; rampant poverty, including among many working people. This is a huge workload for any new administration. Being prime ministerial Critics might say this is Johnson’s single biggest challenge. The leadership process has shown that while he endlessly harked back to supposed successes as London mayor – an often ceremonial role with relatively few powers – Johnson was notably quieter about his period as foreign secretary. Being prime minister is like the latter, to a factor of 10 – a never-ending succession of red boxes containing vital documents, of urgent briefings, of a whole system hanging on your decisions. Johnson has a tendency to ignore advice, pluck statistics out of the air and rely on sudden, cheap glibness. Curbing these long habits will be a daily struggle - his adopting the acronym 'Dude' in his victory speech shows just how hard it is for him. Peter Walker Political correspondent

And their concept of global power is – how to put this diplomatically? – incompatible with the concept of intelligent life.

To understand how this DoBo partnership is likely to function, you need to recall Trump’s excruciating explanation of his kind words about Johnson while standing next to the walking dead that was his predecessor this time last year.

“I said, he’ll be a great prime minister,” Trump told reporters at Chequers. “He’s been very nice to me. He’s been saying very good things about me as president. I think he thinks I’m doing a great job. I am doing a great job, that I can tell you. Just in case you haven’t noticed. But Boris Johnson, I think would be a great prime minister.” Trump went on to say how much he truly, madly loved Theresa May. “This incredible woman, right here, is doing a fantastic job, a great job,” he said. “And I mean that.”

Trump also explored last year what he wanted from a British prime minister pursuing Brexit. “The only thing I ask is that she work it out so that we can have very even trade, because we do not have a fair deal with the European Union, right now, on trade,” he said. “They treat the United States horribly. And that’s going to change. And if it doesn’t change, they’re going to have to pay a very big price, and they know what that price is.”

To be clear: Trump wants his British prime minister to help him get a better trade deal from the European Union that he just Brexited. No problem, Mr President! Have we told you lately what a great job you’re doing?

Back in the real world, Trump wants something else from a trade deal with a newly global Britain. “Very even trade” with Johnson means better access for US farmers to British supermarkets, and better prices for American drugs bought by the socialist NHS.

‘In truth, Boris is not Donald’s best friend in London. Nigel is.’ Composite: Rex

Trump views London as a haven for international terrorists of the jihadi kind, having read lots of tweets from racist British nationalists and watched lots of Fox News. In fact, he told May about all these “no-go zones” when she came to Washington to visit him in early 2017. But one politician – by the name of Johnson, in fact – responded in kind back in 2015. “The only reason I wouldn’t visit some parts of New York is the real risk of meeting Donald Trump,” said the snooty Brit who is now Trump’s man in Downing Street.

Trump’s national security officials hope that Johnson will say nicer things about the game of chlorinated chicken they want to play with Iran. This might be tricky for Johnson, who displayed a Trump-like aversion to work during his tenure as foreign secretary.

“The only reason I wouldn’t visit some parts of New York is the real risk of meeting Donald Trump,” said the snooty Brit who is now Trump’s man in Downing Street.

For some reason, the British national security establishment is unhappy with Trump for withholding intelligence about the airstrikes he planned, ordered and then called off at the last minute. Team Trump said the mission was too rushed to tell their allies, which is fantastically reassuring among Nato allies.

Those same Brits are feeling rather upset at the way Trump forced out their own ambassador in Washington for stating the obvious truth about what Trump calls the fine-tuned machine of his presidency. Which gets us to the core challenge facing Johnson and all the other nationalist leaders trying to cosy up to their role model in the White House. Trump sees the world as a zero-sum game. For a man who clings to America First, there is no room for Britain First; there are only Mini-Me-style tributes to his greatness.

Even in his laziest moments, Johnson surely knows that this poodle-like approach between prime ministers and presidents did not end well for Tony Blair. But that won’t stop Donald from petting him. “We have a really good man who’s going to be the prime minister of the UK now, Boris Johnson,” Trump told a hotel ballroom full of rightwing teenage activists on Tuesday. “Good man. He’s tough and he’s smart. They’re saying ‘Britain Trump.’ They call him ‘Britain Trump.’ And people are saying, “That’s a good thing.” They like me over there. That’s what they wanted. That’s what they need.”

It’s often said that the US and Britain are two countries separated by a common language. But in the era of Donald and Boris, that language is separated from all other Anglophones by things such as grammar, education and brain cells. Who are all these people who don’t know the adjective to describe objects from Britain? Are they the same Britain people who like Trump? Because let’s be honest: there aren’t that many of them. Just 26% of Britain people approve of Trump, according to Gallup, which is around 30 points less than Barack Obama’s lowest point.

In truth, Boris is not Donald’s best friend in London. Nigel is. And for some strange reason Donald can’t help pointing it out every time he talks about the new prime minister.

“I think Nigel is someplace in this audience,” Trump told the young activists on Tuesday. “Where is Nigel? Where is he? Nigel Farage. He’s here someplace. I saw him. I said, ‘What is he doing here?’ He’s a little older than most of you. Where is he? Nigel. Nigel. I’ll tell you what: He got 32% of the vote from nowhere, over in UK. Nigel. Thank you, Nigel.”

So get ready to move over, Boris. You’re an incredible man, and Trump means that. But Nigel, Nigel. Wherefore art thou, Nigel?

• Richard Wolffe is a Guardian US columnist