My appointment with the mayor of London was for 10 o’clock sharp, and I was warned in advance by the young woman in the press office not to be late because Boris Johnson is so very heavily scheduled these days. Any lateness on my part would be subtracted from the 30 minutes, maximum, that I had been allocated. I arrived 10 minutes early, but 40 minutes later Boris still hadn’t shown up in the building. His staff were apologetic. It was most unusual for him not to be on time, they explained, but Boris had been at the Lord Mayor’s Banquet the night before and had decided against cycling to the event in white tie. So he was coming in on the Tube from his home, and must have been held up.

Finally he appears a short while after our interview was scheduled to end. He is not wearing a tie, and I am struck by how tired he looks. Unaware of the story that has been spun to explain his tardiness, Boris mutters apologetically about having had “a million things to do at home”, and having rather overdone it the night before. Then he suggests that his lateness was the fault of the French-owned electricity company EDF, because his home had suffered a power cut that morning, incapacitating his toaster. He wonders, jokingly, if he was being targeted for having written disobligingly about foreign-owned utility companies in a recent column. I tell him that, having once been a colleague of his, I’d have been astonished if he’d been on time, and he pretends to be offended.

Sitting before me gulping coffee in an effort to kick-start his day sits the new “serious Boris”. In truth, the distinction between the old, posh, gaffe-prone Boris the Buffoon and the new cautious, reticent political figure is false. As anyone who has a passing acquaintance with him knows perfectly well, Boris has always been deadly serious in charting his life’s course. From the moment, as a classics undergraduate at Balliol, that he plotted his run for the presidency of the Oxford Union, his vaulting, methodical ambition has been there to see. He dismisses the thesis that he has suddenly got earnest: “I think I’ve paralysed the world with my seriousness for quite long enough. Everyone’s in a narcosis induced by my seriousness.”

Nor is that entirely true, either. Boris elicits a spontaneous enthusiasm from almost any gathering. During a recent impromptu stopover at a south London bus depot, he was mobbed by the drivers, and not just because they wanted to complain about their wages. He is blessed with what might be called a presumption of hilarity. Maybe it’s the shock of straw-coloured hair or the extravagant hand gestures, or the way he puckers his lips before he talks, but people expect what he says to be funny, or mischievous, or indiscreet, so they may even be laughing before he has opened his mouth.

He is not on the greatest form on the day we meet, perhaps because a sense of confrontation is created by the young woman minder from the press office sitting in on our chat and thrusting a tape recorder under our noses. I put it to him that, though it must be great fun for a journalist to become mayor of London, a lot of the minutiae of the job must be very tedious. He recoils theatrically: “I’ll tell you what — it’s a much bigger job than I thought it was going to be.” But he cannot resist ending with a joke: “Every day I awake with a sense of wonderment that the people of London…” Then he checks himself, realising he is sounding like a hack politician and asks self-mockingly: “You know this one?”

Boris later confessed that to get through the Lord Mayor’s Banquet and the interminable speeches by Gordon Brown and others, he had downed the best part of two bottles of wine. Rather than maintain our desultory interview in his office, he suggests we have a game of ping pong. He often has a game in the evening with his aides, lining books up in the middle of his desk as a net. “Are you any good?” he asks, twice, and I see in his eyes the competitiveness that friends have long remarked on. I am spared inevitable humiliation by the press officer, who tells Boris sharply that his next appointment is waiting for him. “Next time you come, we must definitely play some pingers.”

Even with a makeshift ping-pong table in his office, one cannot help thinking that the new king sits somewhat uneasily within his slightly weird new court. Were Boris in his former incarnation as a journalist to travel to City Hall and interview someone else who was mayor, he would certainly have fun.

Norman Foster’s glass monstrosity on the south bank of the Thames is a terrible insult to its neighbour, Tower Bridge, and to the Tower of London across the river. The Glass Gonad, Boris calls his new HQ, while his deputy, Kit Malthouse, is blunter, ranking it as an “architectural jerk-off”.

It is one of those modern buildings that seemed dated even before it opened for business, partly because it is almost impossible and ruinously expensive to clean the glass exterior, so that all the windows are permanently smeared in London grime and bird droppings. Boris’s journalistic eye would have noted the multi-faith meditation room in the basement, the fair-trade organic teas in the canteen, and how the public space of the lower levels is dominated by what looks like a gigantic wheelchair ramp, so that if you want to walk, rather than take the lift, you are forced to trudge pointlessly in wide concentric loops.

But it is the people dementedly punching at their BlackBerrys who seem stranger even than the building. The circle who now surround Boris are not the sort of people he would have known at Eton, Oxford or The Spectator, the weekly magazine he edited, or in the Tory corridors of Westminster during his time as MP for Henley.

The junior ranks of City Hall are young, quite ethnically diverse, idealistic, one senses left-wing, and probably not that exercised by Pericles or any other of the mayor’s classical heroes. After his stunning electoral victory, Boris told Andrew Gimson, who wrote a riotous biography of him, that he would govern London as Emperor Augustus ruled Rome, living in a simple room.

The office he inherited is simple; in fact it’s rather grotty, and because of the strange design of the building, it feels as though you are sitting in a corridor. The building may be grandiose, but the mayoralty is ascetic by design, as Augustus might have had in mind. The mayor of New York has a splendid official residence, but Boris, aside from his £137,000 salary — topped up by £250,000 from his Daily Telegraph column — has nothing. No official car, no security team, not even a mayor’s chain of office. He is wise enough to steer clear of London’s abysmal transport system, preferring to get around on his bicycle.

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