US Vice President JD Vance is taking his holiday in the UK – a trip which will include visits to the Cotswolds, Scotland and, to kick it all off, a few days staying with Foreign Secretary David Lammy at his grace-and-favour country home, Chevening House in Kent.

It would seem an unlikely friendship on the face of it. One grew up in north London, the other in rust-belt Ohio.

One is a left-wing advocate of multi-culturalism, the other a conservative who has, albeit jokingly, referred to the UK as “the first truly Islamist country” with a nuclear bomb.

Yet, despite their differences Lammy and Vance appear to be the best of friends.

As he settled in for a brief chat with the media in the drawing room at Chevening alongside the foreign secretary, Vance spoke warmly of their relationship.

“I have to say that I really have become a good friend, and David has become a good friend of mine,” he said. “Our families enjoy each other’s company very much, which always helps.”

Chevening is set in 3,000 acres of land, including a maze and lake, which was the first destination for the two families on Friday morning, for a spot of fishing.

Vance joked this activity put “a strain on the special relationship” with his children all catching carp, while the foreign secretary came away empty-handed.

Lammy didn’t seem bitter, telling the vice president he was “delighted” to welcome him and his family to 115-room Chevening, which he described as “my home”.

Strictly speaking, the 17th century manor house belongs to the nation, but cabinet ministers, particularly foreign secretaries, are allowed to use it for family getaways or meetings with foreign dignitaries.

The vice president seemed suitably impressed with his friend’s weekend retreat.

Vance acknowledged the two men come from “different political spectrums” but said Lammy had been “kind enough to make time on a visit to [Washington] DC, we got to know each other a little bit then”.

Since that first meeting, when Lammy was in opposition and Vance had just been elected to the US Senate, they have met regularly including at the new Pope’s inauguration in May.

Last week, Lammy told the Guardian he, Vance and Deputy Prime Minister Angela Rayner bonded over drinks in the Villa Taverna, the US ambassador’s residence in Rome.

“I had this great sense that JD completely relates to me and he completely relates to Angela. So it was a wonderful hour and a half,” he said. “I was probably the shyest of the three.”

He said that, like Vance, Rayner and himself were “not just working-class politicians, but people with dysfunctional childhoods”.

Lammy’s parents split up during his teens. His father went to the US and Lammy never saw him again.

Vance told the story of his own upbringing – including an absent father and a mother with a drug addiction – in his bestselling memoir Hillbilly Elegy.

Despite their trickier starts in life, both ended up at prestigious US colleges. Lammy studied at Harvard, where he met and befriended Barack Obama. Vance went to Harvard’s rival Yale – “not quite as good,” Lammy joked at Chevening.

The two men have also bonded over their Christian faith. Vance converted to Catholicism as an adult and attended Mass with Lammy when he visited Washington DC earlier this year.

The pair have something else in common, although neither want to to draw attention to it: their previous less-than-flattering comments about Donald Trump.

JD Vance’s past verdict – “reprehensible”, “an idiot”, “I never liked him”.

And Lammy’s? “A tyrant” and “a woman-hating, neo Nazi sympathising sociopath”.

Be it political expediency or a genuine change of heart, both have since revised their opinions.

But how far do personal relations matter, when there are so many other factors at play – be it national self interest in the case of tariffs, or differences of opinion such as over the situation in Gaza?

Bronwen Maddox the CEO of the Chatham House international affairs think tank says they do, “particularly under this administration”.

“Trump has deliberately personalised these things,” she adds.

That is why Lammy – despite his natural affiliation with the Democratic Party in the US – was tasked with building bridges with their Republican opponents, even before the general election.

Although that might have appeared a tall order, Chair of Republicans Overseas Greg Swenson says his party tend to feel fonder towards the UK than the Democrats.

Vance and Trump have criticised the UK in the past, but Swenson says it “comes from a good place”.

“Both want what’s best for the UK… you never want to see your friend make a mistake.”

However, if Lammy thinks his friendship with Vance is exclusive he may be disappointed.

The vice president is also meeting Conservative leader Kemi Badenoch and Reform UK’s Nigel Farage has hinted that he may be as well.

In between meeting UK politicians, Vance will be squeezing in a trip to the Cotswolds – something that may infuriate those Americans, such as TV chat show host Ellen DeGeneres, who fled to the area specifically to escape Trump and his acolytes.

There have also been reports that singer-rapper couple Beyonce and Jay-Z have been house-hunting in the area.

Explaining the appeal of the region to wealthy Americans, writer Plum Sykes told the BBC’s PM programme it combines the desire for countryside with the need for glamour.

“Americans can’t go to Wales and survive in the same way they can in the Cotswolds where you can get a matcha latte and go to a gyrotonics class.

“The business of the private jet people at Cotswolds airport has gone through the roof.”

Vance is reported to be staying in a house, very close to Diddly Squat – the farm and pub belonging to broadcaster Jeremy Clarkson.

That sets up the possibility of an awkward encounter between the two. Clarkson has previously lambasted Vance, with “a bearded god-botherer” being among his more printable insults.

But a friendship might still flower, after all forming unlikely relationships seems to be as fashionable as the Cotswolds at the moment.