“Boris Johnson delivered the Olympics.” It is a line that is not so much creeping as shoehorning its way into the public debate over Britain’s next prime minister. It is one of Team Boris’s approved lines, when it sends ambitious Tory MPs into the TV and radio studios because Johnson is too conniving to appear himself.

On Thursday night, Kwasi Kwarteng was the latest to come out with it, this time on BBC’s Question Time. Anyone who knows anything about the delivery of the Olympics, and there are hundreds such people around, if not thousands, has the same reaction to this apparent truth. It is to laugh. Boris Johnson himself is among those people. I would be incredibly surprised if his own private reaction to the idea he “delivered the Olympics” would be to anything but chuckle to himself.

I was The Independent’s Olympics news correspondent in the year running up to the 2012 games. I did little else but cover the delivery of the Olympics. The Olympics were, for all intents and purposes, a government department, albeit one with a slightly complicated structure. It was a department in which Boris Johnson, the mayor of London, had no executive role whatsoever.

The question of who delivered the Olympics is also complicated. But none of its possible answers are Boris Johnson.

If the question is, “Who was responsible for bringing the Olympics to London?”, the answer to that is threefold. One, the late Tessa Jowell persuaded Tony Blair and the Labour government that the games were worth bidding for. Two, Seb Coe, for leading London’s ingenious bid. Three, Tony Blair himself, who persuaded the Olympic blazerati, one by one, in a hotel room in Singapore to back London.

If the question is, “Who was responsible literally for the delivery of it?” – the fantastic stadiums, the transport infrastructure upgrades, all built more than on time and to a satisfactory budget – that would have been the Olympic Delivery Authority. The clue is in the name. The ODA was a magnificently run organisation, under its chairman, the softly spoken Sir John Armitt. From 2007 to 2012, it put not so much as a foot wrong.

It was set up, somewhat ironically, as a subsidiary body of the Department for Culture, Media and Sport, whose secretary of state, at least from 2010 onwards, was Jeremy Hunt. If either of the two Tory leadership candidates can claim with an even remotely straight face to have “delivered the Olympics”, it would not be Boris Johnson.

Then there was the London Organising Committee of the Olympic Games, run by Lord Coe. It raised its £2bn budget with ease. It faced some anger over ticketing, but chiefly that was because it organised the most popular Olympic and Paralympic Games in history. Again, Boris Johnson had no role.

Throughout the London 2012 adventure, Boris Johnson made two decisions of any great significance. One was to allow Tory donor Lakshmi Mittal to “sponsor” the games, by building the Orbit statue next to the Olympic Park. It is entirely incongruous to its surroundings. It served no function whatsoever, either during the Olympics or after, other than as an advert for Lakshmi Mittal’s company.

The other came directly after the games, when he personally intervened to make himself chair of the London Legacy Development Corporation. He personally managed the deal with West Ham United Football Club. There is no one, apart from West Ham’s owners, who are also Tory donors, who would consider this deal to be anything other than terrible. It is a complicated saga, many mistakes were made, many of them many years before Johnson’s involvement. But it was he who decided to spend hundreds of millions of pounds trying to make the Olympic Stadium suitable for football. The consensus of opinion is that it is not suitable for football. And the rent paid by West Ham, spread over a hundred years, will still end up being significantly less than the taxpayer has paid to convert it to keep them happy.

The G4S saga aside, which in the end, arguably improved the games, the legacy of the Olympic Stadium (now the London Stadium) itself is its only failure. It is the only aspect in which Johnson was materially involved.

This is not to say his role in London 2012 was not significant. It was. London 2012 made this country feel good, in a way it has not at any other point in its recent history. The London mayor played a significant role in that. He was its head cheerleader, and he did a wondrous job. His detractors still love to share the clip of him stuck on a zipwire in Victoria Park, as if evidence of his being some kind of imbecile. The reaction to the incident at the time was joyful. It was extremely funny.

At the end of the games, he gave an incredible speech outside Buckingham Palace, entirely upstaging the then prime minister David Cameron. As the Pet Shop Boys came out to sing, the crowds really did chant, “We love you Boris, we do! We love you Boris, we do!” I heard it with my own ears.

Where one ranks the relative importance of these contributions is a matter of personal choice. To look back now, the love that was in the air in that incredible fortnight is worth far more than an ugly sculpture and a mess of a stadium. But the idea that Johnson in some way “delivered” the games? Not a chance.

His Olympic contribution is relevant in another way though. Conservatives really do seem to think that Johnson can bring back his feelgood factor of old. If Johnson can win in London, he can win anything, they seem to think. Not a chance.

That Boris Johnson, of 2012, is no more. He is a toxic, divisive figure now. He accepts that himself. Four years after London 2012, the crowds that gathered again for Boris Johnson are the ones that count. They were outside his front door on the morning of 24 June 2016, banging on his car bonnet, and shouting, “scum”.