It was the politics of their style as much as the style of their politics, as President Obama and David Cameron lavished mutual praise at last night's celebrity-packed White House dinner.

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Two hundred years ago British troops invaded Washington and burned down the White House. This year, relations are somewhat friendlier. In fact, judging from the reception David Cameron's been given on his three-day visit to the United States, relations seem friendlier than ever. At last night's state dinner at the White House - the biggest the Obamas have ever held - the two leaders fell over each other to lavish mutual praise: at one point, President Obama described the PM as "just the kind of partner you want at your side".

A-list guest list

On the guest list, to liven up the obligatory political and diplomatic crowd, a host of actors, musicians and businessmen, along with a sprinking of campaign donors. The US wheeled out its biggest star of all, George Clooney - in Washington to speak at Congressional hearings on Sudan. But in a sign of Britain's cultural renaissance Stateside, also present were a clutch of Brits who've proved just as popular over there.

Downton Abbey's Hugh Boneville was there, along with Damien Lewis and Idris Elba, both stars of critically acclaimed US television shows. There was US Vogue's British powerhouse Anna Wintour, and designer Georgina Chapman, who created Michelle Obama's dress for the night. And, along with Virgin's Richard Branson, Apple's designer-in-chief Jonathan Ives.

Cultural fusion

Even the food was a kind of crazy transatlantic fusion: bison wellington, and steamed lemon pudding with Idaho Huckleberry sauce - described lovingly by the chef as "a perfect pairing of US and UK cultures". The White House garden was decorated under a theme of 'America's backyard', designed to showcase the best of both horticultural traditions. And even the instinctively Anglophobe Barack Obama had taught himself a couple of Britishisms, casually dropping "chuffed to bits" into his remarks, and claiming he was looking forward to a good "natter". It was as if Dick Van Dyke was in the room.

But, in contrast to some previous British visits to the US, this trip has gone remarkably well, even if it's been largely ignored by the US press. It's partly down to timing: the two leaders share a mutual interest in the events dominating the world, from Afghanistan and Iran to what's happening in Syria. And for once, in a critical election year, it's expedient for a US President to be seen alongside a Conservative prime minister. A bit of Obama's cool-factor won't have done David Cameron any harm, either.

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Don't mention austerity

The issues which might sharply divide the two: Cameron's austerity versus Obama's stimulus spending in response to the recession, for instance, or unease over the extradition treaty, were pushed to the background. Even the gifts were carefully chosen: a fancy barbecue for Cameron, a table-tennis set for Obama.

Just the kind of partner you want at your side. Barack Obama, on David Cameron

But is there any evidence that Britain in general is enjoying a bit of a moment across the Atlantic? From the media to food, there's plenty of evidence to say yes. Take music stars: there's no greater evidence of British success than Adele, who's spent weeks as US number one. Florence and the Machine and Jessie J are almost as widely feted. So too, the alternative-folk band Mumford and Sons, whose platinum album earned them a spot performing at last night's White House bash. What some pundits are calling the "third wave of British music invasion" was no doubt boosted by the influence of Simon Cowell, whose X-Factor has helped make him part of America's cultural conversation.

Having a moment

In fashion, designers like Stella McCartney and Christopher Bailey are feted by the cream of New York's fashion elite, who've also taken Victoria Beckham to their hearts. Kate Middleton is hailed as a style icon, while some of the most powerful editors in the US fashion press are Brits. Even the once derided Britsh cuisine is the talk of New York right now, with chefs like April Bloomfield taking gastropub fare to new heights in the city at the Spotted Pig and the Breslin.

The last word might go to Huffington Post, which surmised that the Obama/Cameron mutual love-in might as well have been dubbed "Americans and Brits are Just Crazy about Each Other". At this stage in the much vaunted, oft lamented special relationship; flattery, for now at least, will get you everywhere.

Felicity Spector writes about US politics for Channel 4 News