On Boris Johnson’s first trip to meet Joe Biden in Washington, the prime minister was on a charm offensive as he attempts to nurture the special relationship despite their political differences.

Biden has been sceptical about Johnson, partly because of the prime minister’s comments from 2016 claiming that Barack Obama had a bust of Churchill removed from the White House because, Johnson said, of “the part-Kenyan president’s ancestral dislike of the British empire”.

But since Biden came to power the two men have struck a cordial tone, finding common ground on the Aukus defence pact and the climate crisis, though dividing lines between the US Democrat and British Conservative remain.

Climate

Johnson made clear en route to the US that he wanted to galvanise action towards a successful outcome at the Cop26 climate summit in Glasgow in November – a goal shared by Biden. In particular, the UK was hoping for more progress towards the target of $100bn in climate finance for developing countries, set more than a decade ago.

The prime minister suggested there was only a 60% chance the target would be met before the summit, but the odds were significantly shortened after Biden announced on Tuesday that he was doubling the US’s contribution to $11.2bn. Johnson welcomed Biden’s climate funding pledge as a “very good start” that took them “a long way towards the goal”.

With many countries yet to announce fresh emissions reduction targets, and no confirmation that the Chinese president, Xi Jinping, will attend the summit in person, Biden and Johnson are likely to discuss how best to secure a deal that keeps a 1.5C limit on global heating within reach.

While their politics are radically different, Johnson has stressed that both men would like to spark a “green industrial revolution”, tackling the climate crisis while creating hundreds of thousands of jobs in clean energy.

Afghanistan

The fraught withdrawal from Afghanistan raised profound questions about the relationship between the US and the UK, with London apparently kept in the dark about Washington’s intentions at key moments in the crisis.

The prime minister was forced to resort to publicly lobbying Biden to delay the US departure to allow more time for the evacuation to take place – a request that fell on deaf ears.

The two men are unlikely to have dwelt on past misunderstandings, instead focusing on discussing how to deal with the new Taliban government and whether a humanitarian crisis in the region can be averted.

Geopolitics

The US, UK and Australia blindsided allies by announcing Aukus, a defence and security alliance for the Indo-China region. France reacted with fury, withdrawing its ambassadors from Washington and Canberra for consultation – pointedly leaving out the UK, which it has dismissed as the “fifth wheel” in the alliance.

Johnson is keen to show the pact is more than an attempt to placate Washington and reflects the UK’s strategic interests. Biden is hawkish on China, and eager for the world’s democracies to form fresh alliances – he will host a virtual “leaders’ summit for democracy” in December.

Johnson echoed that approach by inviting countries including Australia, India and South Korea to the G7 summit in Cornwall in June, making a wider group that the UK has suggested could be a “D10” of major democracies. After meeting Biden, Johnson was due to dine with the Australian prime minister, Scott Morrison, to hail the Aukus deal.

Travel

Downing Street had been frustrated by the US travel ban applying to the UK, and lobbied for change. But it appeared to be blindsided by Monday’s announcement that the US would lift the ban for the UK and many other countries.

Fully vaccinated people will now be able to travel to the US without having to quarantine, but key details of the policy remain ambiguous, including whether the US will accept the AstraZeneca vaccine and whether children will be exempted.

Johnson was expected to press Biden on these questions on Tuesday, but No 10 was pleased that the overarching restrictions are being ditched. The UK has sought to claim some of the credit for the change of policy, pointing to a bilateral travel taskforce that has met since the summer, but the new regime applies equally to scores of countries.