As so often happens, the second date went better than the first. President Obama, who had seemed rather cool towards Gordon Brown in Washington a few weeks ago, went the other way yesterday. He showered Mr Brown with praise: the special relationship was extraordinary, lasting, wonderful. And Britain itself was wonderful – and sunny! And, oh yes, he loves the Queen!

They are over the surname stage now. It’s all Barack this and Gordon that. First Gordon told us that Barack was his personal friend. As he said this, Barack did The Stare, a look that leaders are trained to do for these events: head turned, gaze level, smile lurking. Then Barack told us that Gordon was his new best friend. Gordon tried to do The Stare but just ended up looking adoring. We are talking labrador here. As Donny Osmond so memorably sang: “And they call it puppy lo-o-o-ve.”

The event had begun nervously. Gordon’s opening speech was as rushed as a groom late for the church. In contrast the President was positively languid. He offered little titbits of personal info. He’d had a chat with Gordon’s sons about dinosaurs. At one point he began swigging from a water bottle. Gradually Gordon began to relax. His face, which seemed overly made up with rather pouting orangy lips, looked almost bashful. It occurred to me that this event may be the apex of his political career.

He looked transported. In Washington there had been no press conference, only a “pooled spray” where hacks shouted from behind a sofa. But yesterday they had the whole nine yards, as the Americans say. They had the Locarno room, a bling-fest of Empire, plus lecterns, flags (eight), hundreds of journalists, lights, cameras, action. In the front row, Hillary Clinton, in blinding blue, was accompanied by young Davey Miliband.

Now we know what comes after the pooled spray: the total gush. Old Faithful, the geyser at Yellowstone, would be jealous of the sheer force of the output. This, for instance, was Gordon. “It’s been an extraordinary visit already and I’ve benefited from Barack’s advice not just about elections, but about fitness! We’ve been talking, not the treadmill of politics but the treadmill that we’re both on every day, the running machines!”

This set Barack off on another gush. The sheer level of his charm is fascinating. This, for instance, was his take on President Sarkozy’s petulant threat to walk out of the G20. It was all a media fantasy. “I know that when you’ve got a bunch of heads of state talking, it’s not visually that interesting,” he said. “So there’s a great desire to inject some conflict and some drama into the occasion. But the truth of the matter is I think there has been an extraordinary convergence!”

The media fantasy didn’t seem quite so imaginary a few hours later at the day’s other main event – the Sarko-Merkel press conference. If the morning event was dignified and adult, this was playtime. They too had flags – French, German and EU – and a sheen of glamour the Anglo-Saxons just don’t have.

The children were not very happy. They speak with two languages but one voice. They have “red lines” and they want them met. They want tax havens named and shamed, hedge funds regulated, financial transparency. “We demand results, we want hard and fast results,” Sarko said, practically levitating with energy.

“This is nothing to do with ego or temper tantrums,” said Sarko as he stamped his tiny (well, OK, petit) foot. I could almost see Gordon and his new best friend laughing about that.

Times Recommends

• Milk: do we need a dairy godmother?
• DIY: the women doing it for themselves
• First double portrait of Princes unveiled