President Donald Trump's first state visit to Britain comes fraught with the possibility of diplomatic peril, with a Conservative Party leadership contest as well as differences over Huawei and Iran likely to test the resolve of the so-called "special relationship." The president and his wife, Melania, arrived in the U.K.on Monday to begin their three-day trip. It will include a private lunch and banquet dinner at Buckingham Palace with Queen Elizabeth II, tea with Prince Charles and a visit to Westminster Abbey. The visit comes at a time when cracks are widening in the trans-Atlantic relationship, with political analysts concerned his "off-the-cuff" and "impulsive" leadership style could make matters worse over the coming days. "I would say the special relationship is certainly on shaky ground," Cailin Birch, global economist at the Economist Intelligence Unit, told CNBC via telephone.

Indeed, just before touching down at Stansted Airport, Trump took to Twitter to blast London Mayor Sadiq Khan, who in a weekend opinion piece likened Trump to the fascists who roiled Europe in the 20th century. "He is a stone cold loser who should focus on crime in London, not me," Trump said of the mayor. Trade disputes with countries across the world demonstrate the U.S. president's "America First" approach to bilateral partnerships, Birch said. He added that Trump's combative approach to traditional Western allies represents a "fundamental shift" in U.S. foreign policy. Some in the U.S. and U.K. have prided themselves on sharing a cultural, political and commercial bond that has long been called the "special relationship." The phrase was first used in 1946 by then-Prime Minister Winston Churchill, with the U.S. and U.K. having overcome the global turmoil, terror and loss of life of World War II together. The relationship has since then been marked by ongoing commercial and cultural links, helped by a shared language and a willingness to join in military operations, the fight against the Islamic State militant group in Syria and Iraq being the most recent example. But with Trump in the White House, the conventional rules of diplomacy have been ripped up and the dynamic between the U.S. and the U.K., and the rest of the world, is changing. Whether the "special relationship" can survive appears increasingly uncertain.

Leadership contest

Birch highlighted the Conservative Party leadership contest as one potential diplomatic pitfall, with the U.S. president "unlikely" to show much respect to what he sees as a lame-duck leader. Prime Minister Theresa May announced the timetable for her resignation last month, finally bowing to intense political pressure over the country's Brexit impasse. She will remain as prime minister until after Trump's visit is over, with a replacement set to be appointed over the coming weeks. Ahead of his visit to the U.K., Trump suggested he might meet with Brexit Party leader Nigel Farage and Conservative lawmaker Boris Johnson.

Foreign Secretary Boris Johnson arrives at Downing Street ahead of the weekly cabinet meeting on July 3, 2018 in London, England. Dan Kitwood | Getty Images

In an impromptu exchange with reporters at the White House on Thursday, Trump described them both as "friends" and "good guys." The U.S. president has since reaffirmed his admiration for Johnson, who is currently the bookmakers favorite to replace May. "I know the different players. But I think Boris would do a very good job. I think he would be excellent. I like him. I have always liked him," Trump told the Sun newspaper in an interview published Friday.

Huawei

"The important thing to understand is that the special relationship is not really about the president and the prime minister," Jacob Parakilas, deputy head of the U.S. and Americas program at the think tank Chatham House in London, told CNBC via telephone. "Having said that, there are a few issues that pose fairly substantial risks to its core elements." One of those issues, and the "most urgent" according to Parakilas, is a simmering dispute over Chinese telecommunications giant Huawei. Britain has indicated Huawei would be allowed a restricted role in building parts of its next generation 5G communication network. The network is set to bring faster internet speeds and lower lag times — it has tremendous potential to change the way people interact with new technologies.

The U.S. has told allies not to use Huawei's equipment because of fears it could be used by the Chinese for spying, accusations the telecoms giant has categorically denied. Last month, it was reported the British government would allow Huawei to build out parts of its 5G wireless networks, which would defy U.S. demands for a blanket ban. Trump is reportedly poised to tell the British government in person that Washington may limit intelligence sharing with the U.K. if it allows Huawei to build part of its new 5G network.

Iran

The other "big issue" for U.S and U.K. officials to discuss, according to Parakilas, would be what to do next when it comes to Iran. Speaking shortly before Trump's visit to Britain, U.S. National Security Adviser John Bolton said the "threat was not over" from Iran and the country would be "held accountable." His comments came amid intensifying tensions between the Trump administration and Western allies, including Britain, over the Iran nuclear deal.