“So, have ya Brexited yet?” Blunt, folksy and utterly unconventional, the question down the phone line to Theresa May was pure Trump. As an icebreaker, it is hardly an easy opener for a woman whose entire premiership has been created, and dominated by, the UK leaving the European Union.

More than two years after the British public narrowly voted to quit the EU, the country still hasn’t “Brexited”. May’s latest plan for a continued close relationship with the 27 other nations in the bloc has caused resignations and rebellion within her own party.

In many ways, Trump was simply asking a question Leave voters themselves have asked many times. But US Presidents don’t usually use a transatlantic phone call on an encrypted line to ask a question that the Prime Minister could hear in any pub. And what’s just as surprising is that Trump has used this opening line not just once, but several times since he entered the White House.

“It’s like Groundhog day, like you’ve never met him before,” one former staffer said. “It’s not like the usual small talk. It’s every time he starts the call. Everyone rolls their eyes as if to say ‘you know nothing’, but of course Theresa just sidesteps it.”

As Theresa May prepares to meet Trump at her Chequers country house on Friday lunchtime – the key government meeting of his fraught visit to the UK – she and her team were braced for more curveballs.

Trump underlined his unpredictability in spectacular fashion on Thursday by giving the Sun newspaper an extraordinary interview in which he suggested May had refused to listen to his advice to have a ‘clean’ Brexit.

Asked about the compromise plan to keep the UK closely aligned with the EU on things like goods, the President said: “If they do a deal like that, we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal.

“I would have done it much differently. I actually told Theresa May how to do it but she didn’t agree, she didn’t listen to me. She wanted to go a different route.”

Still, No.10 have pulled out all the stops in trying to design an itinerary that will put the President in a very good mood. A black-tie dinner at Winston Churchill’s ancestral home in the gorgeous English countryside; a top-secret demonstration of a joint counter-terror exercise between US and UK special forces; tea with the Queen at Windsor Castle; and golf at his own course in Scotland.

It may sound like the perfect VIP holiday. But for May, the four-day “working visit” is all about just that: working. For the PM, it is not a PR opportunity. Far from it, given how unpopular Trump is in the UK.

No, the guts of the trip for Downing Street is when the two leaders sit down for talks at May’s official residence in Buckinghamshire. On the official agenda will be Russia, trade, Brexit, and the Middle East, No.10 says. Aides are hoping he sticks to the brief and offers some progress in each area.

But in another indication of how unorthodox this Presidency is, and how they lack a personal connection, May and Trump are expected to spend just 10 minutes on their own. They will then be joined by the new Foreign Secretary, Jeremy Hunt, and others for a “working lunch” over Dover sole, Chiltern lamb and meringue pie.

It’s then on to the press conference, where Downing Street will hope the President doesn’t create any more controversy than he has already. At a Nato event on Thursday, he managed to suggest May’s Brexit wasn’t as hard as the public wanted and highlighted the political “turmoil” experienced by his host (“I’m going to a pretty hot spot right now, right? With a lot of resignations”).

Of course, the whole trip is a direct consequence of the fact that May was the first foreign leader to visit Trump in Washington back in January 2017. At the time, the PM offered a full State Visit on behalf of the Queen, but although that offer still stands, this week’s downgraded version was deemed more suitable.

Back then, there was almost a desperation in No. 10 to beat every other leader to shake Trump’s hand. Several sources say that the offer of a State Visit was the brainchild of May’s former chief of staff, Fiona Hill.

When Trump and May met over lunch in the White House, a strange exchange unfolded. The President was on script, telling her how pleased he was to have her visit, because his Scottish mother loved the Queen and loved the UK.

But then, according to one eye-witness, Trump’s National Security Adviser, Mike Flynn, tried to ease the conversation by mentioning that other leaders had wanted to be the first through the door. Vladimir Putin was among them. This prompted Trump to say: “You didn’t tell me that. Why not?” He then proceeded to harangue the former general, while May and her team looked on, amazed.

“It was jaw dropping, the whole thing, from beginning to end,” one former insider says. “It’s like pinning jelly to a wall. He has got no attention span, in fact I thought he had some kind of ADHD by the time we left. He was all over the place. And his team are so subservient to him, yes sir, no sir. It was pathetic, grown men like [Mike] Pence acting like puppies.

“Trying to have consistent conversations was difficult. It was like the Little Britain sketch where he would wander and then suddenly you were ‘back in the room’.”

The pair were fresh from their first joint press conference. It had not been an easy ride for the President, with the BBC’s Laura Kuenssberg asking about his “alarming beliefs” on the torture of prisoners, abortion, banning Muslims and closeness to Russia.

Trump then started the lunch with another characteristic question. “So, who do you think won that then?” he asked May. 

“He sees everything as a battle,” says one source. “You’re either winning or losing. Then he launched into a few minutes of a rant about Laura Kuenssberg and how the BBC didn’t treat him fairly. It was unlike any other politician that you would meet.”

He then followed up with another ‘icebreaker’ that stunned several of those present, asking for views on abortion term limits.

“The overwhelming impression you got was this was someone who was completely naïve about the world of government. At one stage he even said ‘Theresa, I get these briefings every day, you wouldn’t believe it!’

“She must have thought ‘I think I would, you know.’ He has a frightening ignorance and naivety on the one hand allied to an incredibly strong view that basically government is just like business. And you run it like a business. And you put business people in charge.”

Trump told his British guests at the lunch: “I am going to bring in this guy Tillerson [Rex, his first Secretary of State]. You’re going to love him, you’re going to love him. The State Department is just about making deals and Tillerson is the best deal maker I know.”

The eyewitness continued: “He just loves to talk. He said he didn’t like Angela Merkel and predicted she was going to lose [her election in 2018 – she won]. You are sitting there slightly agog, coming from a British system where everything is different anyway.

“But overall it was really him being undiplomatic and really like a golf club bore. She was incredibly diplomatic, batted things back. Sometimes she’s just a pro and she was really a pro for that whole hour.”

Before the press conference, May and Trump met in the Oval Office. She had got him to agree that he would continue to support Nato, and not to lift sanctions on Russia over its military action in Ukraine. Craftily, she then mentioned his private remarks in the public Q&A, forcing him to commit to his pledges on the record.

“She was a dream, she totally nailed it, she was on the money,” one aide said. “I think he came away thinking she got the better of me, she surprised me – and I won’t be put in that position again. He thought she’s this sweet little old lady and she got what she wanted. She basically released a private conversation in public.”

But the triumph was short-lived for May’s team. Within minutes, photo agencies released the infamous picture of her hand being held by Trump as they walked to their lunch. “The hand hold blew all that out of the water,” one former official said.

May was depicted not as someone who had gently outmanoeuvred the President, but as his handmaiden. To make matters worse, Trump had failed to tell the Prime Minister that he would within minutes of her departure sign an executive order to ban Muslims from entering the US.

Yet for all his disdain of convention, May has learned some of how the President works. Offering something concrete is the way to his heart. Her decision to increase British troops numbers in Afghanistan recently proved the UK’s commitment to Nato. The fact that the UK is one of the few Nato nations spending the 2% GDP spending target is another key asset.

However, an eagerness to please the Trump White House is not always universally popular, or workable. HuffPost has been told that before the visit to Washington in January 2017, May’s former chief of staff Hill proposed doubling the UK’s spending on defence to 4% of its income.

The rise would have cost many billions, and Chancellor Philip Hammond went “berserk” when told of the plan. It was swiftly dumped, but in a supreme irony that 4% figure is precisely the one Trump floated at this week’s Nato summit as he harangued his European allies for not paying their way in return for US the defence umbrella.

It’s not security protection, but protectionism on trade that most worries some members of the May government. Trump’s ‘America First’ rhetoric could mean that the cherished prize of a UK-US trade deal is a distant prospect.

Former National Security Adviser Sir Peter Ricketts says that it would be wrong to underestimate the wider American interest in getting a better deal.

“There is a risk that if we look too demanding of an early trade relationship, the very hard headed US trade negotiators will drive a hard bargain and that’s not just Trump, that’s the way the US trade system works. 

“I think the argument we’ve got to win is America gains by having a strong and prosperous Europe. That’s not what he believes but it doesn’t mean we don’t develop the argument.”

In November, Wilbur Ross, the US commerce secretary, said ominously that any deal should “[take] into account our commercial interests”.

Given the problems with private US firms wanting a slice of the NHS pie and its farmers wanting to import GM crops, some in Whitehall now think that the best the UK can hope for is not a comprehensive trade deal but sector specific agreements for financial and legal services.

One former insider says: “Trump never gives anything away for free. He’s spent a life in business screwing people. He wants his money back, he wants his jobs back, and there’s no reason why he would offer us anything.”

Ricketts adds: “We’ve got to expect Trump will keep on banging the ‘America First’ drum. We’ve got to adjust to that. We have to keep making the arguments for things like a climate change treaty and free trade.

“We’ve got to hope that when he’s made his point and he’s come home with some ‘wins’ then things will ease off. With China and trade, he goes in hard, bids high, he’s a tough deal maker, but if you can come back with something that is progress then you can perhaps encourage him not to take his steps all the way.”

At the Blenheim Palace dinner with US and UK businesses looking on, May’s first words of welcome to Trump on Thursday were pretty transactional themselves.

Pointing out the two nations were the largest investors in each other’s economies, “with over a trillion dollars of investments between us” she rammed home that the UK is the largest investor in the US, “providing nearly a fifth of all foreign investment in your country”.

“We invest 30% more than our nearest rival. More than 20 times what China invests. And more than France and Germany combined.

“That all means a great deal more than simply numbers in bank accounts. It means jobs, opportunities and wealth for hardworking people right across America,” she said.

All British Prime Ministers prove useful to American Presidents when they need a bit of global PR at election time. And May deliberately singled out a string of swing states where Britain could prove very useful.

“Tomorrow morning, around 24,000 men and women in Michigan will get up and go to work for a UK-owned company. Another 40,000 will do the same in Ohio. 60,000 in Pennsylvania.

“In Texas, British employers provide work for an incredible 100,000 people.”

Chris Wilkins, May’s former speechwriter, explains that her big speech in to the Republican Retreat in Philadelphia, the day before her White House visit in 2017, was deliberately designed to set the wider terms of the ‘special relationship’.

Her speech was peppered with references to strong links forged by another female Conservative Prime Minister, Margaret Thatcher, and Ronald Reagan.

“We wanted to build bridges with the Republican mainstream, knowing where the President was going,” Wilkins says. “It was really about saying ‘you know what, whatever the personalities, this relationship remains strong’.

“The Reagan and Thatcher references were all about that. We have a shared history and a shared approach and when our two nations step up and lead it’s good for the world. When we don’t, others, Russia and China, will.

“We know he’s not in that Republican mainstream. In many ways the speech repudiated some parts of the Trump agenda.”

Wilkins, who drafted May’s famous ‘Nasty Party’ speech all those years ago, said the plan was clear.

“Our main concern when we went there was American isolationism. As we step back, others step up. In many ways it was a response to the [‘America First’] inauguration speech [the week before].”

“It was an attempt for the PM to triangulate being the first person across the Atlantic to meet the new administration, but recognising the ambivalent nature of public opinion at home. 

“At the time the focus groups showed and think the same now…the majority opinion is that ‘we don’t really like this guy, but we get that America is our closest ally and we have to have a relationship with them’…that’s the line the PM was trying to walk.”

For all these reasons, Downing Street is more prepared for the Chequers meeting in a way it wasn’t for the Washington trip.

Those phone calls with Trump have continued to both surprise and almost exasperate. But she’s stuck with it.

One former staffer says an example is the way the President continually takes up valuable phone time attacking the Scottish First Minister. She has made clear her loathing of his politics, and her predecessor fell out with Trump over his golf course developments.

“He totally hates Nicola Sturgeon. He spends lots of his time bitching about Sturgeon. He loathes Salmond too. But why spend so much time talking about Sturgeon in a phone call with Theresa May?”

Some of May’s former staff think she can be too accommodating at times. During the general election campaign he launched at Twitter attack on London Mayor Sadiq Khan.

“I felt she should really strongly have backed Sadiq then and said he was wrong,” the staffer says. 

“And she didn’t and it really frustrates me because Trump values that sort of thing, who values strength. He likes the pitched battle in a sense, that’s what he respects. She sort of fudged it, I think that’s wrong domestically but also in terms of the way you deal with him.”

May learned her lesson and later in the year did indeed challenge him. She earend a rebuke, but aides think it was worth it to put down a marker.

“Theresa @theresamay, don’t focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom,” the US president had tweeted. “We are doing just fine!”

Yet despite the latest slights and Brexit resignations, the PM will still try to get something tangible, however small, out of the visit this week.

“People underestimate that ability to withstand this stuff. Other people get too personal and too offended by these things, she’s doesn’t let it bother her. She just brushes it off. It doesn’t linger in a way it does with others,” one admirer said.

“In some ways, it’s so refreshing a politician that’s not driven absolutely bonkers by their own media, whereas Trump obviously is.

“In these dire times, it’s a strength that she will plough on and she will try and get the prize she want. She will ignore the silly things he says and have her eyes on the prize. She’s smarter than him and she may just navigate round him again.”

When Trump arrived by helicopter at Winfield House on Thursday afternoon, the US ambassador’s residence located on the edge of Regent’s Park, he was greeted by Beatles music. “We Can Work It Out” was among the classic tunes that had famously helped the Fab Four conquer America.

But it seems like Theresa May’s own soundtrack for the trip, though the Chequers summit will reveal whether Trump is in the mood to reciprocate. Will he want to win, or work it out?