Boris Johnson has flown back to the UK after his transatlantic jaunt reassured about his personal relationship with Joe Biden after the pair sought to put the chaos of the Kabul airlift behind them with face-to-face talks in the Oval Office.

The warm personal rapport that characterised Johnson’s relationship with Donald Trump – who called him “Britain Trump” – was not obviously on display as he and Biden briefly addressed the press before retiring for private talks. Biden told an involved anecdote about travelling more than a million miles on Amtrak, which US reporters revealed he has wheeled out on several other occasions.

Once the press had been forcefully ushered out by White House media handlers, however, witnesses said the pair held constructive talks. They discussed expanding the Aukus pact – announced last week – into a broader alliance that could cover other areas of shared interest, including safeguarding human rights, technology and expanding open markets.

And on Capitol Hill, Johnson took the opportunity to try to soothe concerns about the operation of the Northern Ireland protocol, saying he remained committed to the Good Friday agreement.

But news that the UK has all but abandoned hopes of a bilateral free trade agreement with the US underlined the fact that to bond with Biden, Johnson has had to trim his ambitions to fit the president’s agenda.

The arch dealmaker Trump used to boast about the prospects for a trade agreement with the UK, but Biden has a packed legislative agenda at home that will take precedence over trying to win congressional backing for a complex set of trade negotiations.

As well as taking on China – essentially the purpose of the Aukus pact – the two countries are both committed to tackling the climate crisis, and in doing so, creating more green jobs in their own economies.

Johnson’s hopes of securing a successful outcome to the Cop26 climate summit in November that keeps 1.5C of warming within reach took a significant step forward when Biden doubled the US’s contribution to climate finance. When the prime minister met Biden’s vice-president, Kamala Harris, they were able to agree that the $11.2bn US climate pledge made it, as Johnson put it, “a great day for the world”.

Other tangible gains from the visit were harder to come by: Johnson said he had won the backing of the president to lift the ban on British lamb exports, though consultations are ongoing and no formal decision has yet been announced.

No 10 was also keen to claim credit for the lifting of the US travel ban, claiming a bilateral “travel taskforce” that has been operating since the summer had helped to change the Americans’ minds. But the changes apply equally to scores of countries.

The UK government appeared to have had little warning that the decision would be announced on Monday morning, and was left scrambling to establish the details, including whether AstraZeneca jabs would be accepted under the new system.

But Downing Street will be happy to bank the intangible benefits of a closer rapport with the US – and Johnson, no fan of Zoom calls, returns to the UK energised by three days of the kind of politics he likes best: up close and personal.