“I’ve got you a chat with Boris,” the press officer whispered conspiratorially to me, covering the 2009 Boat Race for The Times, and my colleague from the Telegraph. “But just the two of you,” he added. “Don’t tell the others.”

This seemed odd. Boris Rankov, that year’s race umpire, was an approachable fellow. Why the secrecy? We wondered what news Rankov was about to reveal. The discovery of an unexploded mine off Chiswick Eyot, perhaps, or a decision to throw out any rowers doing a degree in land economy?

It was a bit disappointing, therefore, to be shown into a room and find not a professor of Roman history and six-times winning oarsman but another Boris, blond not bald, who shared the umpire’s love of classics but had no apparent interest in boats. The mayor of London gave some rah-rah-rah about the capital and said how great it was that the Olympics would use the alma mater’s lake. It didn’t make either paper. It was, though, the first time I met our future leader.

A Prime Minister has rowed in the Boat Race, but not a British one. Henry Waddington, born near Le Mans and educated at Rugby, was in the Cambridge crew in 1849. Thirty years later he was prime minister of France for 11 months.

But Boris Johnson was not a boatie. If he had attended the race as a student it would have been to nick a policeman’s helmet, in time-honoured Wooster fashion. To adapt the Eton Boating Song, the only “swing-swing together” that probably interested Johnson was with his body between someone’s sister’s knees.

At Eton he was a dry bob, excelling at the Wall Game in his own chaotic and physical way. “Completely non-directional, he has to be pointed in the right way or he may push the wall over,” a school report said in 1980. A year later, it was noted that he played “like an echidna [a type of spiny anteater] on heat”. In 1982, when he captained the Collegers, he was called “the blond behemoth”.

He had this in common with Harold Macmillan, his fellow OE PM, who was more fearless than his bookish image suggests. This is the man who spent ten hours in a shellhole in 1916 with a bullet in his pelvis, dosing himself with morphine and Aeschylus. Seven years earlier, Macmillan had played his part in an historic Wall Game: the last time a goal was scored in the big St Andrew’s Day match.

Other prime ministers have had sporting talent. Alec Douglas-Home played first-class cricket for Oxford and Middlesex. Wisden reported that he was good against spin and useful on a sticky wicket, which may have helped in politics.

John Major was no less keen, if less capable. At a summit in 1991, he opened the batting in a charity match with Bob Hawke, the Australian prime minister. Hawke kept stealing the strike but Major didn’t mind until the umpires waved them off after a few overs.

“Time for real cricketers,” the umpire said. As they walked in, Major asked Hawke if he’d known they would get limited time. “Jeez, yes,” Hawke said. “Didn’t you?”

David Cameron was a decent college tennis player, described by John Bercow, his doubles partner for the Commons team, as “like John McEnroe when he made a mistake but tolerant and encouraging when I did”. Winston Churchill was public schools champion at fencing. Clement Attlee played billiards for Oxford. And Ted Heath won the Sydney to Hobart yacht race on Morning Cloud in 1970 before leading Britain to victory in the Admiral’s Cup a year later while prime minister.

The Johnson approach to sport — and politics — differed from his predecessors. He had the same enthusiasm and desire to win: he just didn’t care whether he did it within the rules. Johnson once said his tactics in the Wall Game were “sudden spasms of uncontrolled aggression”.

Maurizio Gaudino would agree. The former Germany midfield player was taking part in a charity football match in 2006 when a red-shirted Johnson, playing, as the Telegraph put it, “like a demented combine harvester”, ploughed into him with a no-hands rugby tackle. At least Gaudino was a grown man. In 2015, Johnson barged shoulder-first into Toki Sekiguchi during a rugby exhibition in Tokyo, sending the 10-year-old child flying. “I accidentally flattened him, unfortunately,” Johnson said. “But he bounced back.” The boy said he was “in pain but OK”.

This gung-ho competitiveness extends to the tennis court, where Johnson plays with a warped wooden racket that sends the ball off at unpredictable angles and puts opponents off with his deep gorilla grunting, and to the annual cricket match between his family and Earl Spencer’s, for which he has been known to select such distant cousins as Kevin Pietersen and Monty Panesar.

Johnson would doubtless agree with Vince Lombardi’s dictum. “Show me a good loser,” the American football coach said, “and I will show you a loser.”

It reminds me of a story told by my former Times colleague, Philip Howard, about his father, Peter, who captained England at rugby in the 1930s. Losing to Ireland at half time, he gathered his team. “Now look here chaps, are we going to play like proper Englishmen in the second half?” he asked. “Or shall we try to win?” There then followed the filthiest 40 minutes of foul play. Though England still lost, by one point, I suspect Johnson would have approved of the spirit.