Andrew Grice: They had a mutual interest in making trip work – and it did

They don't need to act; the bonhomie is real," one British minister said, reflecting on David Cameron's bonding with Barack Obama as his three-day visit to the United States ended last night.

The Prime Minister and his team were surprised that the red carpet was rolled out for an extra mile. It seems the US President was very moved by the reception he received in London last May – not least from the Queen – and wanted to return the favour.

On the face of it, the PM and president make an odd political couple. But they had a mutual interest in ensuring the trip was a success. It suited a president described by his critics as the most left-wing one in modern times, to be best pals with a Conservative leader as he prepares to seek re-election. It did Mr Cameron no harm to be seen on the world stage being feted by its most powerful leader.

Relations between the US Democratic Party and the Conservatives were in the deep freeze in the 1990s but those tensions are now forgotten. Mr Cameron's socially liberal views have more in common with the Democrats on issues like gay marriage than a right-wing Republican movement.

Right-leaning Tories keep lines open; Liam Fox has been helping Mitt Romney's bid to win the Republican presidential nomination after resigning as Defence Secretary last October. But it was significant that Mr Cameron avoided meeting any of the Republican hopefuls.

Mr Cameron has always tried to play down the "special relationship", believing his two Labour predecessors spent far too much time fretting about it. Yet this week's visit showed it is still special, not least because of the unique military and intelligence links. Mr Obama said Mr Cameron was "just the kind of partner that you want at your side," adding: "I trust him."

The two leaders are on the same page on withdrawing from Afghanistan and discussed how to stay there. "We don't have a veto on the US pull-out but we have asked them for no surprises," said a British source. They will hope to remain in tune on Syria and Iran, though an Israeli strike on the latter could provoke a different split for Mr Cameron – with his Liberal Democrat Coalition partners.