Rarely since the time of George Canning in the 1820s has a British foreign secretary faced such potentially conflicted relations with an incoming US administration. And rarely has Britain’s foreign secretary, a post now occupied by Boris Johnson, been arguably so ill-equipped to deal with resulting tensions.

Like Johnson, Canning was a Eurosceptic. He was critical of the so-called “Concert of Europe” dominated by conservative regimes in Prussia, Austria, Russia and post-Napoleonic France. Canning famously declared that by opposing European colonialism in Latin America, “I called the New World into existence to redress the balance of the Old.”

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But Canning’s stance was severely tested by the emerging power of the United States, symbolised by the 1823 Monroe Doctrine, promulgated on his watch. Not wholly unlike Donald Trump, President James Monroe declared the US would go its own way, and told Britain and the other great powers to keep out of its business and its hemisphere.

Johnson’s talks with senior Trump aides on Sunday, and his meetings on Monday with Republican leaders in Congress, are likely to have illuminated starkly different approaches to major issues that even a more experienced minister would struggle to overcome. Insofar as its policies are known, the Trump administration poses serious challenges to British interests in key areas.

The most obvious divergence concerns Russia. Theresa May, Britain’s prime minister, has identified Vladimir Putin’s regime as international public enemy number one. Speaking in October, she called for a “robust and united European stance in the face of Russian aggression” and the “sickening atrocities” for which Putin was responsible in Syria.

Britain’s anxieties extend to Russia’s military buildup on Europe’s eastern frontiers, its landgrab in Crimea and meddling in Ukraine and other “near abroad” former satellites, and its cyber attacks and information warfare. The murder in London of a former KGB agent, Alexander Litvinenko, continues to sour relations. Security chiefs have warned that Britain could be targeted by Russia in the same way as the US during last year’s presidential election.

But Trump sees matters very differently. He continues to broadly reject the findings and advice of US intelligence agencies concerning Russian election meddling, and loses no opportunity to swap compliments with Putin. Any US-Russia rapprochement, pursued independently of London, could impose extraordinary strains on Anglo-American ties.

Trump’s iconoclasm extends to Nato, which Britain regards as a vital defence against Russian expansionism. By suggesting the US might not militarily assist threatened Nato members, for example the Baltic states, Trump and his aides are recklessly encouraging Russian aggression – at least as Britain’s defence chiefs see it.

Any deal accepting Russia’s annexation of Crimea would likewise be seen as undermining international law and the authority of the UN, by which London sets great store.

Trump is hostile to another landmark international agreement close to Whitehall’s heart – the painstakingly negotiated, multilateral 2015 nuclear deal with Iran.

Unlike the US, Britain has since re-established full diplomatic relations with Tehran. Bringing the country in from the cold, and restoring its position as a regional partner for the west, is a long-cherished British objective. Trump threatens all that.

While reluctant to unilaterally disarm, successive British governments have strongly supported international nuclear nonproliferation efforts. Curbing the spread of weapons of mass destruction is seen as essential in dealing with unpredictable regimes such as North Korea.

Trump, in contrast, has spoken of the desirability of Japan, a close British ally, and South Korea acquiring nuclear weapons, principally to deter North Korea – although he may also have had China in mind.

When Kim Jong-un, North Korea’s dictator, recently boasted his long-range missiles would soon be able to carry nuclear warheads, thus theoretically threatening US territory, Trump’s response was crudely provocative. “It won’t happen,” he tweeted. Analysts are still trying to work out what he meant.

May’s government, like David Cameron’s before it, has gone to extraordinary lengths to woo the Chinese government, ignoring abuses in Hong Kong, Tibet and China’s Muslim west in an effort to attract inward investment. While Britain shares US concerns about China’s island-building in the South China Sea, Trump’s taunting of Beijing over this issue, as well as trade and Taiwan, potentially undermines efforts to build a new “golden era” in Sino-British ties – unless, of course, Britain disowns him first.

Other key areas of divergence include attitudes to the UN as the world’s premier rule-making body, upholding universal human rights, and the vital need, as London sees it, to build bridges rather than erect walls between the west and the Muslim world. Trump’s mooted racial and religious-based curbs on immigration could result in some British ministers and MPs being banned from travel to the US. His unquestioning pro-Israel, pro-settlements stance may bring more tensions, despite May’s recent trimming.

On other issues, Trump and Britain agree. One is the necessity of defeating Islamic State and similar jihadi terrorist groups. But Trump’s penchant for protectionism does not sit well with Johnson’s push, as Britain leaves the EU, for new free trade treaties, not least with the US. If, like Canning, Johnson hopes Trump’s New World will help rebalance Britain’s relations with the Old, he could soon be sorely disappointed.