BRISTOL, England — On Aug. 19, 2016, Arron Banks, a wealthy British businessman, sat down at the palatial residence of the Russian ambassador to London for a lunch of wild halibut and Belevskaya pastila apple sweets accompanied by Russian white wine.

Banks had just scored a huge win. From relative obscurity, he had become the largest political donor in British history by pouring millions into Brexit, the campaign to disentangle the United Kingdom from the European Union that had earned a jaw-dropping victory at the polls two months earlier.

Now he had something else that bolstered his standing as he sat down with his new Russian friend, Ambassador Alexander Yakovenko: his team’s deepening ties to Donald Trump’s insurgent presidential bid in the United States. A major Brexit supporter, Stephen K. Bannon, had just been installed as chief executive of Trump’s campaign. And Banks and his fellow Brexiteers had been invited to attend a fundraiser with Trump in Mississippi.

Less than a week after the meeting with the Russian envoy, Banks and firebrand Brexit politician Nigel Farage — by then a cult hero among some anti-establishment Trump supporters — were huddling privately with the Republican nominee in Jackson, Miss., where Farage wowed a foot-stomping crowd at a Trump rally.

Banks’s journey from a lavish meal with a Russian diplomat in London to the raucous heart of Trump country was part of an unusual intercontinental charm offensive by the wealthy British donor and his associates, a hard-partying lot who dubbed themselves the “Bad Boys of Brexit.” Their efforts to simultaneously cultivate ties to Russian officials and Trump’s campaign have captured the interest of investigators in the United Kingdom and the United States, including special counsel Robert S. Mueller III.

Both inquiries center on questions of Russia’s involvement in seismic political events that have shaken the world order, with the European Union losing a key member and U.S. voters electing a president critical of Washington’s traditional alliances.

In Britain, recent revelations about Banks’s Russian contacts have triggered scrutiny of whether the Russians sought to bolster the Brexit effort. In the U.S., congressional Democrats who recently obtained a trove of Banks’s communications have begun exploring a different question: Did the Brexit leaders serve as a conduit between the Kremlin and Trump’s operation?

Banks rejected the notion that he was a go-between, insisting his contacts were routine business and diplomatic exchanges — and that the investigations are a “witch hunt.” But he acknowledged that the interactions raised reasonable questions about whether the Brexiteers were “a back channel to the Russians,” as he put it.

“The only problem with all of that is that not one shred of evidence has been produced. . . . It doesn’t go anywhere,” Banks said in one of two interviews with The Washington Post in Bristol this week.

Asked whether Russians had been probing them or seeking to win influence or intelligence, Banks conceded, “They may have. But if so, it wasn’t a very good probe.”

Throughout the 2016 campaign, the wealthy insurance executive built a first-name rapport with the Russian ambassador as Banks briefed him on the breakaway campaign — exchanging frequent, chummy texts and emails, and meeting with him in person four times in about 12 months, according to Banks. At the same time, he and other Brexit backers also intently pursued entree to Trump’s world, according to interviews and dozens of emails and text messages Banks provided to The Post.

As both relationships deepened, Banks and his associates discussed Trump’s bid and the U.S. presidential campaign with Yakovenko, the Brexit backers acknowledge. At least two of the meetings between Banks and the ambassador came shortly before or after meetings with Trump.

In recent weeks, British parliamentary investigators have sought information about Banks’s relationship to Russia and allegations that he was offered financial inducements, including a potentially lucrative gold-mine deal with a Russian businessman he met through the Russian ambassador.

The interactions between the Brexit leaders and the Trump campaign have also drawn the interest of Mueller as part of his investigation into Russia’s interference in the 2016 campaign, which is examining contacts between Trump associates and Russians.

Two people — former Trump communications official Michael Caputo and another person, who spoke on the condition of anonymity because of the ongoing investigation — told The Post that Mueller’s investigators asked about Farage’s relationship to Trump associates in witness interviews this year, including Caputo just last month.

A spokesman for the special counsel declined to comment.

Meanwhile, congressional Democrats are examining the role of the Brexit leaders after a whistleblower gave a cache of documents detailing Banks’s interactions with the Russian ambassador to members of the House Intelligence Committee earlier this month, according to three lawmakers on the panel.

Rep. Adam B. Schiff (Calif.), the top Democrat on the committee, said he has questions about whether Banks and his associates “served as a conduit of information to and from the Russians on behalf of the Trump campaign.” Another committee member, Rep. Joaquin Castro (D-Tex.) said the material “opens a whole new chapter” in the ongoing inquiry into Russian efforts to intervene in the 2016 U.S. election.

A White House spokesman did not respond to a request for comment. Bannon, who led Trump’s campaign in the final months of the 2016 race, declined to comment.

Trump’s lawyer, Rudolph W. Giuliani, said he was not aware of any questions from Mueller about the Brexit backers and had seen nothing about the topic in documents he has reviewed. “I never heard anything about the Russian ambassador [to London] nor have I ever talked to the president about this,” he said.

Farage and Banks said they have not been contacted by Mueller’s investigators and disputed the idea that they ferried information for the Trump campaign or the Kremlin.

“There seems to be a culture of throwing hysterical accusations around without any evidence whatsoever,” Farage said in an email response to questions.

Banks said he and his fellow Brexit leaders have sought to be transparent about their dealings with Russia. Shortly after Trump’s election, he said, they reached out to officials from the U.S. Embassy in London in the wake of a report suggesting they were pro-Russian actors.

Banks said he and Farage each met once with American embassy officials to describe their contacts. Their associate Andrew Wigmore said he sat down with U.S. diplomats five or six times and turned over numerous documents.

A spokesman for the U.S. Embassy in London confirmed that leaders of the Brexit movement met with American diplomats, including Thomas E. William, a top political officer at the State Department, but declined to discuss the subject of the meeting.

Banks said he was releasing documents to The Post to show he has nothing to hide, and he said he would be happy to speak to Mueller.

“We had so much fun at a parliamentary select committee,” he said, referring to his recent appearance before British lawmakers. “We’d love to be called in.”

The connections between the men who would become the Bad Boys of Brexit and Trump’s future inner campaign circle stretch back to 2013, when Farage said he first met Bannon — then at the helm of the far-right website Breitbart. The conservative media executive quickly bonded with the populist politician, who at the time was leading the UK Independence Party, an anti-immigration, make-Britain-great-again force that helped fuel a backlash against the European Union.

Soon, the Brexit leaders also began to forge Russian ties.

In the fall of 2015, during UKIP’s annual convention at the Doncaster racecourse several hours north of London, Wigmore, a Farage confidant, met a Russian diplomat named Alexander Udod, who then helped arrange a lunch for the UKIP leaders with the Russian ambassador, Yakovenko. (Udod was one of 23 suspected Russian intelligence officers ejected from Britain this year after the nerve agent attack against Sergei Skripal, a Russian double agent, and his adult daughter, in Salisbury in south England.)

Banks and Wigmore said they were interested not only in briefing the Russians on Brexit, but also in seeking possible Russian backers for their various offshore investments, including banana plantations in Belize.

In November 2015, the two men had what they describe as a “6-hour boozy lunch” at Yakovenko’s fashionable residence in London.

The two men briefed the ambassador on their Brexit plans, but Yakovenko seemed most interested in hearing stories about Wigmore’s father, who had been involved in one of the last Britain-Russia spy swaps, Banks said.

Over tea at the ambassador’s house a few days later, Yakovenko introduced Banks to a Russian businessman, who pitched him on a potentially lucrative merger of six gold mines. Banks passed on the opportunity, he said, months before the Brexit vote was scheduled.

“I’m a businessman. . . . Why wouldn’t I?” Banks said of his willingness to consider the deal, saying it had nothing to do with Brexit or Trump.

Reports in The Times of London, The Guardian and its Sunday paper, The Observer, about the proposed gold-mine deal and some of the correspondence between the Brexit backers and the Russians have prompted questions in Britain about whether the proposal might have been a way to route Russian money into the Brexit campaign or compromise its backers.

Wigmore, who also served in a diplomatic post with the High Commission of Belize in London, said his main goal at the lunch was not to talk about Brexit, but to help find a buyer for a large Belizean banana plantation whose owner had been designated as a drug kingpin, effectively preventing the farming operation from major international markets.

“In hindsight,” Wigmore said, “it looks more ridiculous than it actually sounds.”

The Russian embassy in London did not respond to requests for comment, but it has denied that it had any involvement in Brexit.

“The Russian embassy has not in any way intervened in the domestic UK political process, including the Brexit referendum,” the embassy told The Observer. “Meeting stakeholders representing all political spectrum of the host country is a natural element of the work of any embassy.”

After the initial encounters, the Brexiteers were quickly on a first-name basis with the ambassador.

“Dear Alexander,” Banks wrote in a text message the day after their lunch. “Firstly many thanks for the hospitality. I thoroughly enjoyed myself. Beautiful wine and food.”

He went on to invite the ambassador to his “Old Down” manor home in the countryside, a sprawling estate and country park with gorgeous views and llamas. Banks said the visit never took place.

“At the time, the Russians weren’t considered the baddies at all,” Wigmore said. “In London, everyone was engaging with the Russians.”

Indeed, in the months to come, George Papadopoulos — one of then-candidate Trump’s volunteer foreign policy advisers who is now cooperating with Mueller’s probe — also sought a meeting with Yakovenko. In March 2016, according to emails and U.S. court records, Papadopoulos unsuccessfully worked to land an introduction to the Russian ambassador through a London-based professor and other Russian contacts.

Around that time, Farage’s movement suffered a blow in Britain, losing a competition to be the official government-financed campaign urging people to vote to leave the E.U.

So he and his allies struck out on their own, funded by Banks, an insurance and mining magnate. He ended up putting 9 million British pounds into the campaign, Banks said. The effort was boosted by enthusiastic support from Bannon’s Breitbart, which by then had launched a Britain edition and was promoting Farage and the long-shot Brexit initiative with vigor.

On June 23, 2016, the Brexit forces eked out a victory. Suddenly, Farage was an international celebrity. The following month, Farage — who had stepped down from his UKIP leadership post — and his associates attended the Republican National Convention in Cleveland. There, they were greeted as conquering heroes and began to make inroads into Trump’s campaign.

One night during the convention, Farage was introduced to Trump’s longtime adviser, the infamous political trickster Roger Stone, at an Italian restaurant, according to both men. Stone, who was accompanied that night by the Internet radio host and conspiracy theorist Alex Jones, said Farage’s main goal appeared to be to get a meeting with Trump.

The next day, Stone said, he tried to help by calling his former business partner, Paul Manafort — then Trump’s campaign chairman — and suggesting that the Republican nominee get together with Farage. Manafort’s response was something along the lines of, “I’ll put a good word in,” Stone recalled.

It was another encounter, however, that would get Farage and his allies the Trump meeting they wanted.

On the last night of the convention, Wigmore and Farage wandered into the bar at the Hilton Hotel, where they ran into a rowdy group of staffers for Mississippi Gov. Phil Bryant (R).

“They were in­cred­ibly drunk. And the assistant to the governor said, ‘Look, if we invite you to Mississippi, would you come?’ ” Wigmore recalled in an interview. “Of course, we said, ‘Yes, of course,’ not thinking it would be followed up. But it was.”

In an emailed statement, Bryant said: “I admired the Brexit movement from afar two years ago. I believe the same principles that drove Brexit contributed to President Trump being elected. Both events restored hope to the forgotten men and women.”

The Brexiteers returned to London upbeat about the prospects of more closely aligning their movement with Trump’s. Less than a month later, their ties to his operation were further cemented when Farage’s biggest American booster — Bannon — was installed at the helm of Trump’s campaign.

Two days after the Bannon announcement, Wigmore and Banks lunched with the Russian ambassador and discussed Trump’s prospects and their upcoming trip to Mississippi.

“We had no idea that we would meet [Trump], but I’m sure we would have told the Ambassador we were going,” Wigmore said in an email to The Post. “I do remember him stating that he did not think [Trump] had a chance of winning and you may remember at the time Trump was 10 points down in the polls and the attacks on him were full on.”

Less than a week later, in Mississippi, Wigmore said Farage met Trump for the first time at a high-dollar fundraiser for the GOP campaign in Jackson.

Afterward, Trump invited the Brexiteers to a campaign rally and asked Farage to speak on stage.

“Trump says, ‘I’ll come on stage, I’ll speak for a few minutes, then I’ll introduce you. You speak for six minutes, and then I’ll carry on. Are you okay with that?’ ” Wigmore recalled.

Soon, Farage had the hyped-up crowd on its feet.

“If I was an American citizen, I wouldn’t vote for Hillary Clinton if you paid me. In fact, I wouldn’t vote for Hillary Clinton if SHE paid me,” Farage told an audience that roared its approval. “Folks, the message is clear, the parallels are there. . . . Remember, anything is possible if enough decent people are prepared to stand up against the establishment.”

From then on, Farage and his cohorts became almost de-facto Trump campaign surrogates. They attended presidential debates in St. Louis and Las Vegas and a rally in Michigan. When the campaign was rocked by The Washington Post’s report on a videotape in which Trump bragged about groping women, Farage went on Fox News to defend him. “He’s not running to be Pope,” Farage declared.

On Nov. 12, 2016 — four days after Trump was elected president — Farage and his colleagues decided on a whim to pay a visit to Trump Tower in New York.

They arrived at the building without an appointment or an invitation, Wigmore said, and Farage called his pal Bannon, who responded: “Yeah, obviously, come along and see me.”

The whole retinue of Brits ended up in a lengthy meeting with the president-elect, whom Banks described as “very un-Trump-like” that day, “very relaxed, open-neck shirt . . . very reflective.”

“He wanted to talk to Nigel about what it felt like when he finished the Brexit campaign, and it was a very mellow kind of conversation,” Banks said.

Eventually, Farage — the first foreign visitor hosted by the president-elect — would take a now famous photo with a smiling Trump, Banks and Wigmore in front of the building’s gilded elevator.

During their visit, the Brexiteers got a glimpse of Trump’s chaotic operation, listening with amusement as harried staffers argued over who should be named White House chief of staff, Banks said.

At one point, Wigmore said, a secretary standing outside the office blurted out: “You’re British. Do you have a number for Number 10?” — a reference to the British prime minister’s home at 10 Downing Street. In fact, Banks did. But he wanted something in return, and Trump’s staff was happy to oblige: a good telephone number for Trump’s presidential transition office.

A few days later, after Banks had returned to London, he and Wigmore sat down again for tea with Yakovenko, the Russian ambassador — their fourth meeting in a year.

The Russians “were utterly gobsmacked that Trump had won,” Banks said.

Wigmore had been handing out the Trump transition team’s telephone number to all sorts of diplomats from various countries, he said. So when the Russian ambassador asked for the number, he said he happily obliged.

Wigmore said he was “not thinking there was anything remotely sinister” in sharing information he had learned at Trump Tower with the Russian diplomat. “Why would I?”

Booth reported from Bristol, England, and London. Craig Timberg, Alice Crites, Josh Dawsey and Julie Tate in Washington and Karla Adam in Bristol contributed to this report.