It was David Cameron’s annual summer garden party for Westminster journalists. Amid the dry white wine and canapés, the Prime Minister stood regaling reporters about his latest extraordinary encounter with the Mayor of London.

Earlier that week, Cameron explained, the pair had sat facing each other in the Cabinet Room, with Johnson outlining his plans for London and requests for help. Then, as Cameron started responding, with help from a sheaf of briefing papers, Johnson leant across the table. “What’s all this? Let’s see!” he cried as he tried to snatch the documents from the PM’s grasp. Cameron held on to his precious notes, and for a few moments the two Conservative politicians wrestled and tugged for supremacy across the cabinet table, like a couple of immature schoolboys. Officials looked on in astonishment. It was hugely undignified, yet hugely symbolic.

David Cameron and Boris Johnson were once schoolboys together, of course, at Eton in the early 1980s. Johnson was a King’s scholar, known to everyone in college with his striking blond hair and a cleverly manufactured persona as an eccentric toff. Cameron, two years younger and weaker academically, was not widely known beyond his house. If either was going to become the 19th Prime Minister to come from Eton it would surely be Boris (although his name, too, was adopted for effect – family and long-standing friends called him Al, short for his first name, Alexander).

I first met Johnson not long after his Eton days, when I visited the Oxford Union for a debate in 1984. In my opening remarks I made the mistake of comparing him to a Dulux dog. Nobody laughed, at least not until Johnson shot back with a quick, witty response. I still bear the scars. He’d put me in my place. I’ve been careful with him ever since.

Cameron didn’t arrive at Oxford until a year later. The two Etonians were famously members of the boisterous upper-class dining club, the Bullingdon. They appear together in the famous photo that must have been republished a thousand times.

For a while about ten years ago the Oxford photographers Gillman and Soame tried to stop anyone publishing it by withdrawing their copyright permission. I was working 
on Newsnight at the time and came up
 with the wheeze of getting an Oxford
artist called Rona to paint her “impression” of the photo, and then
 we filmed her doing so. We had a lot
 of fun with that picture; Rona sold her copyright far and wide, and even reproduced it on tea towels.

I looked hard for some political arm-twisting behind the Bullingdon photo ban. Johnson certainly wouldn’t have asked for it to be banned – as a journalist he’s relaxed about such things, whereas Cameron gets uptight at every mention of Eton or the Bullingdon. But it’s still unclear where the instruction came from.

Both men are from upper-middle-class families, but Cameron has stronger links to the British aristocracy. Johnson has spent his life pretending he’s rather more upper class than he really is, calculating, perhaps, that the British public love a toff, especially if he’s unthreatening, dishevelled and bumbling. Cameron, in contrast, tried to play down his privileged background. He hates any suggestion of being “posh”. He never forgave me when, during an interview during the 2005 leadership contest, I asked him, “Who’s your nearest male relative who didn’t go to Eton?” “Ah,” he said with a moment of hesitation and look of panic, “Well, there’s a cousin of mine. I think he went to Marlborough.” He was kicking himself afterwards. “I should have known you’d ask something like that.”

Both men entered the
 Commons together in 2001, for Oxfordshire seats where previous MPs – Douglas Hurd and Michael Heseltine – had been prominent pro- Europeans. But both had earned reputations as Eurosceptics – Cameron as an adviser to Norman Lamont on Black Wednesday and later to Michael Howard. Johnson achieved fame as Brussels correspondent of The Daily Telegraph with a stream of articles highly critical of the EU.

Johnson was among the first to back Cameron for Conservative leader in 2005, but once he was installed as Mayor of London three years later, the two men would become rivals for Tory affections. Every autumn at party conference Johnson would turn up, met at the station by a media scrum who’d been advised of the precise time of his train. Then for 24 hours all the talk was of how loyal or disloyal he’d been to Cameron in his two big speeches.

Some see Johnson’s declaration in favour of Brexit as another calculated move, albeit a huge gamble – one that almost matches Cameron’s big risk in holding the referendum in the first place. The friends and allies of 2005 are now seemingly adversaries to the death, as Cameron increasingly came to fear Johnson as the only man who could really destroy his leadership.

According to Ken Clarke (whom he backed for leader in 2001), Johnson coming out for Brexit may have been a deliberate ploy both to destabilise Cameron, and to reinforce his position as darling of the grassroots when the PM calls it a day. Some say that could be within weeks if Britain votes to leave. Clarke said last month with surprising candour that Cameron “wouldn’t last 30 seconds if he lost the referendum”. Johnson hasn’t enjoyed a great referendum so far. His comments about Barack Obama’s “part-Kenyan ancestry” were widely considered crass. But the ultimate prize may be within his grasp. He may never get a better chance than this. Could Alexander Boris de Pfeffel Johnson be PM by Christmas?

Boris v Dave: the Battle for Europe airs tonight at 9pm on Channel 4