In recent weeks, Boris Johnson’s allies began to prepare the ground for a Joe Biden presidency. They argued that, while there might be some short-term turbulence, the two men would have more in common than we might think.

As Downing Street joins the rest of the world in a nervous waiting game for the US election result, the well-worn official line is that the US-UK relationship will remain strong in any scenario, though the reality is more complicated.

“We are confident that it will go from strength to strength whichever candidate wins the election,” Dominic Raab, the foreign secretary, told Sky News this morning. With masterful diplomatic understatement, Raab acknowledged “slightly different contours of the opportunities and the risks” depending on the eventual outcome.

If Donald Trump defies the odds and hangs on, Johnson would still enjoy a personal bond with the US president, even if it hasn’t yet translated into tangible gains for the UK. A Trump second term would revive hopes of a US-UK trade deal. This was always one of the Brexiteers’ great hopes, but negotiations have stalled over the UK’s reluctance to allow agricultural imports, such as chlorine-washed chicken and hormone-injected beef. So a free trade agreement would be far from easy; if Johnson made concessions to Trump, he would provoke strong opposition at home, undermining his recent reassuring signals to the farming and food standards lobbies.

Some Johnson allies would privately welcome the survival of a fellow populist, and detect a message that should worry Keir Starmer: offering solid stability, even in a global crisis, is not enough, and you must inspire voters, too. Yet many Conservatives would be jittery about Trump’s unpredictability on the world stage and hostility towards global institutions. They would quietly breathe a sigh of relief if Biden made it to the White House.

If that happens, initially at least, there would probably be what one Whitehall official called “some bumps in the road”. Johnson would be unlikely to win the beauty contest to have the first telephone call or first invitation to Washington. His team would profess not to care about such media obsessions, but of course they do. Biden, who believes Brexit was a mistake, would be more interested in rebuilding US links with the EU, so Emmanuel Macron and Angela Merkel would be high on his “must call” list. There might be a struggle between France and Germany to be top dog. Outside the EU, the UK has no hope of playing the role successive prime ministers coveted as a bridge between Europe and America.

Personal relations between Biden and Johnson would be awkward initially. The former vice president will remember Johnson’s suggestion that Barack Obama’s opposition to Brexit stemmed from being “part-Kenyan” and having an “ancestral dislike” of the British empire. UK officials were unable to forge the usual links with the challenger’s team ahead of Tuesday’s election, though this was mainly due to the Biden camp’s wider wariness following Russian intervention in the 2016 presidential contest.

Tensions cannot be dismissed as all in the past. Johnson angered Biden in September by threatening to override the Northern Ireland protocol in the EU withdrawal agreement. Biden, who is proud of his Irish roots, warned bluntly the UK could forget about a US trade deal if it undermined the Good Friday Agreement.

Although the PM would never admit it, a Biden presidency would increase the pressure on Johnson to reach a compromise with the EU as trade negotiations reach a critical stage. He could then dump the controversial provisions on the protocol in the Internal Market Bill, and avert a damaging rift with the incoming president. Despite that, there would be little prospect of a US-UK trade deal with Biden in the White House. It would not be a priority for his administration. Ministers believe a more realistic hope would be the UK (and the US) joining the trans-Pacific trade partnership.

In the medium term, Johnson aides believe events would enable him to build a good working relationship with Biden. The UK holds the rotating presidency of the G7 next year, ensuring a presidential visit to the UK. Johnson’s plan for a D10 group of democratic nations to tackle China’s influence – adding countries such as India, Australia and South Korea to the G7 – might dovetail neatly with Biden’s foreign policy goals.

Luckily for Johnson, he will host the COP26 UN climate change conference in Glasgow in a year’s time, allowing him to work closely with Biden, who would champion the issue and rejoin the Paris agreement.

Johnson could take some comfort that the close security and intelligence links between the US and UK transcend presidents and prime ministers who do not enjoy a strong personal relationship. The bumps in the road would be uncomfortable, but would eventually be worth it.