Their first encounter had been a brush-by in the VIP lounge of the G20 conference centre in Hamburg during the morning. President Putin had intended it to be the briefest of handshakes, forgetting there is no such thing as a quick handshake with Donald Trump. The US president had thrust out a clammy right paw, grabbed hold of his arm with his left hand and then pumped it enthusiastically for rather longer than was comfortable. The man clearly has no sense of personal space.

Vlad flashed a half-hearted smile, keen not to look outmanoeuvred by such third-rate power games. The Donald might be a great deal taller than him, but he is also badly out of shape. A physical wreck. One judo throw and Trump would be on his back. Where he belonged. Had he really gone to all the trouble of trying to rig the US presidential election for this? Maybe he would have been better off with Hillary after all. At least you could have an intelligent conversation with her.

G20: Donald Trump and Vladimir Putin conclude lengthy meeting - live Read more

By the time the two world leaders met for their bilateral meeting in the afternoon, Putin was better prepared. For the obligatory photo opportunity at the beginning of the talks, he and Trump were seated in adjacent armchairs with translators and officials to one side. Their body language could hardly have been worse. The Donald was perched on the edge of his chair, trying to appear in control though just looking a bit needy. Vlad sat back in his, determined to make little or no eye contact. He wanted to make the American president sweat and he was succeeding. There was no doubt who was the boss now.

The Donald is uncomfortable with lengthy silences and started filling the void with words. Any words. “We’ve had some very … uh … very good talks,” he began. “We’re going to have a talk now and obviously that will continue.” Putin looked down, trying not to smirk. They both had Russian-to-English translators but the Americans had clearly forgotten to bring an English-to-English translator.

“We look forward to a lot of positive things happening for Russia and for the United States and for everyone concerned,” Trump continued. “I’m delighted and it’s an honour to meet you, Mr President.”

Sensing he might already be out of his depth, Trump remembered the first rule of diplomacy his advisers had told him just that morning. If things feel tricky, do another handshake. You can’t go wrong with a handshake. The American president stuck out a hand, which Putin accepted. This time the Donald kept his other hand by his side. Round one to Putin.

Now it was the Russian president’s turn to reply. He stared at the floor, his voice seldom rising above a mumble. Trump’s eyes darted from side to side, unsure of where to fix his gaze. He wasn’t used to having to concentrate for more than 140 characters at a time. And even that was often a struggle.

“We spoke over the phone,” Vlad said. And he’d listened in to a great many more conversations that had been tapped. “But phone calls are never enough definitely. I’m delighted to be able to meet you personally.” His lifeless monotone and blank expression suggested otherwise. “And I hope, as you have said, that our meetings provide positive results.” Not that he was holding out much hope. As he finished, the Donald went for a second handshake. Vlad made sure this was even more perfunctory than the previous one. Round two to Putin.

The opening speeches concluded, a few reporters started shouting out: “Will you be talking about how Russia tried to rig the US election?” before they were bundled out the room. Putin shrugged. Somehow he doubted it. The US president might be all mouth in slagging off the Russians behind their backs, but Vlad was confident he was no trousers face to face.

Putin relaxed. He had 17 years of playing international hardball under his belt: Trump only had a few months. It would be no contest. Yes it would be annoying having to talk about Ukraine with someone who wasn’t entirely sure where it was, but he could deal with that. Better still, he could drag it out for an hour longer than the 30 minutes that had been scheduled. By the time they were finished, Trump would be a puddle on the floor.

While the world’s two most powerful men were the star attraction, the British prime minister found herself rather left on the sidelines. Theresa May had arrived far too early for the group photograph of the G20 leaders and had wandered about looking a bit lost. The G20 was rapidly turning into a G19 + 1 for her. At the plenary session she had tried passing a note to Trump – “Do you still love me? I’m not really that cross with you about the Paris climate agreement” – but he had blanked her. The only time she had really contributed was to tap the US president on the shoulder to let him know he was facing the wrong way.

The people most interested in the Maybot were the UK press who wanted to know if she felt rather marginalised. Channel 4’s Matt Frei also asked if, when critics called her robotic and heartless, they had misunderstood her.

“I think what’s important is that we get on with the job and getting on with the job is delivering for people,” the Maybot replied. We can take it that’s a no, then. Her critics haven’t misunderstood her.

Have Trump and Putin met before? We know for sure that Friday's meeting was their first since Trump became president, but it is not clear whether it was their first ever.

Over the past few years, Trump has variously claimed to have either met Putin and “got along great”, or to have never met him.

His account of their relationship began to change during the US election campaign: • 2013: David Letterman asks Trump whether he has met Putin personally. "He's a tough guy. I met him once," Trump replies. • 2015: Talk-radio host Michael Savage asks Trump point-blank whether he has ever met Putin. "Yes," Trump says. "One time, yes. Long time ago." He adds: "Got along with him great, by the way."

• November 2015: Trump says he got to know Putin "very well" during a joint television appearance on 60 Minutes. Trump's segment had been taped in New York, Putin's in Russia. • July 2016: At height of the election campaign, Trump tells reporters: "I never met Putin, I don't know who Putin is." • July 2016: Pressed by George Stephanopoulos in an interview on ABC, Trump says: "I don't think I've ever met him. I mean if he's in the same room or something. But I don't think so." Putin has denied meeting Trump, telling Megyn Kelly on NBC in June: "There was a time when he used to come to Moscow. But you know, I never met with him."

• This article was amended on 12 July 2017. An earlier version mistakenly referred to the “BBC’s Matt Frei”. Frei is at Channel 4.

