He has a devilish, wicked, lopsided little half-smile, does Mr Barack Obama, and the instincts in his face want him to use it. Just as well, really, because it pulls him back into the realm of humanity, and without it we might be in danger of trading hallelujahs and tugging his frayed hem.

'He's not the President,' reprimands the copper keeping crowds at bay outside the House of Commons. 'Yes, he is!' wails a fat white sunburnt American. 'He's my President! Let me throooough, man, let me through!'

'He's not the President,' comes the (angrier, screechier, more frustrated and didactic) cop's reply. 'He's a ...'

I think he went on to get it right, roughly, didactically, in the sun. He is not the President yet. A visiting dignitary. But, oh, how I wanted this copper to be a great fan of The Life of Brian and continue... 'He's a very naughty boy.' Because there was something utterly messianic about the visit yesterday to London of what polls increasingly have down as the United States' next President. Not least the presence of mortals gathering to be sprinkled with stardust, PMs and PMs-in-waiting among them.

Barack Obama said a few things yesterday, and said them well. There was a rather significant mention of the 'transatlantic' alliance, as opposed to the 'special relationship' that we Brits seem to get so high on; a taut and careful and supremely successful nuancing of the Europhilia he possesses and which gives liberals hope. Rather than boring on with soundbites about the 'special relationship', he simply talked - hesitantly sometimes, but always thinking - of what Britain and America have in common. He spoke of the rule of law and due process, before adding, more winningly: 'We just like the people! There is a deep and abiding affection for the British people in America and a fascination with all things British that's not going to go away any time soon.'

He wants, as he said in both France and Germany, some help with troops in Afghanistan, while wanting to get out of Iraq. Again, the nuancing. He also spoke, unheedingly, of the 'stalwart' assistance given by British troops.

But, mainly, he simply appeared, and sprinkled that stardust. Gordon Brown could be seen beaming. In the dark. The dark of the hall of 10 Downing Street. Obama wasn't allowed, through protocol, to grasp Mr B's hand outside for the cameras, as he is only a presidential candidate, and it wasn't done for John McCain's visit. But there was an Obama arm swiftly around Gordon's shoulders, and a (rather fluid) returning lower-back pat, before the door shut. Asked, a little later, about Brown's prospects, he said thoughtfully: 'You're always more popular before you're in charge. Once you're responsible, you're going to make some people unhappy.'

Gordon and Barack walked together - a few minutes out at the back of Downing Street around St James's Park. Apparently they talked about economies, global warming, terrorism, Middle East stuff. Obama had been up at about four in the morning to do the same thing at breakfast with a tired-looking Tony Blair. Apparently Obama sleeps for four hours every night.

In the garden there was something going on. Psychologists have a word for it - mirroring? Transference? Both had dark suits, done up with one button in the middle, and white shirts, and silky reddish ties, their left hands in their pockets, and their right hands gesturing, constantly. Back in the garden, Gordon waved his right hand to show him various trees. Nobody quite knows why. Nor what he was saying. The crueller watchers had it down pat. 'That tree's going to vote for me ... that one's dithering.' That was possibly a little too cynical, because our Prime Minister did indeed seem to be genuinely, sunnily, smiling. Twenty minutes later, Obama met David Cameron in the grounds of the Commons, and Cameron did the same. Waved his arms and showed him shrubs. Don't they have trees in Illinois?

Mr Obama is now the world's most recognisable phenomenon. There were, by 11 yesterday morning, hundreds of fans standing in King Charles Road, round the corner from Downing Street, cameras and phones held high. There were banners: 'Mr B Obama you are a ray of hope 4 billions of young men and women around the globe'. There were tears, really. Crying. Logos. Slogans. Hope. The woman on the Clapham omnibus quite literally rose to her feet. A big old belching red number 88 was the first vehicle stopped at 12.44 as Obama's convoy fled the gates of Westminster to head back to Illinois. She stood up, earrings and sunglasses bouncing, shouting through the glass, furiously snapping away on her phone, ecstatic. The woman on the Clapham omnibus is our 'How will it play in Peoria?' in America. I almost tried to find her. We like to have names. But the bus was going, for once, too fast, leaving on the retina only the shimmering slick of an advertising flyer for, I assume, a film called Space Chimps Go Bananas. There was a cartoon monkey. Disappearing fast. Perhaps you want to provide the Bush metaphor?

And now Mr O, with his wickedly easy smile, has been flying, home, and very possibly listening to Leonard Cohen, and smiling. First we take Manhattan. Then we take Berlin.

It's all gone rather well. And you are going home, sir, very possibly to a historic victory on 4 November, and this was a canny little trip, so well-judged, and your aides will be enjoying a Scotch or two on the way. Why wouldn't you want to smile?