First it was men from the West Midlands police wearing "PC Pleb" T-shirts. Then Tom Newton Dunn, the "political editor" of the Sun, turned up at the Liberal Democrat conference in a T-shirt that said "I'm a pleb" (actually he's an Old Etonian: class in this country is, if nothing else, a source of rich comedy). And then Ed Miliband shouted "Pleb!" across the Commons at David Cameron.

All the rough and tumble of politics, you might think, even when it ended a man's cabinet career. The only trouble was that this contemptuous merriment was probably a falsehood. Last Friday, a third police officer was arrested in connection with what is still sometimes absurdly called "plebgate", and on Monday night further evidence will be presented by Dispatches on Channel 4, which has already made the running with this story – the true story, that is.

On 19 September Andrew Mitchell, the chief whip, was prevented by policemen from taking his bicycle through the gates of Downing Street as he usually did, and he irritably remonstrated. In the twinkling of an eye the Sun reported he had called the police "plebs", and the Daily Telegraph printed the supposed police log of the incident: "There were several members of public present, as is the norm, opposite the pedestrian gate, and as we neared it, Mr Mitchell said: 'Best you learn your fucking place … you don't run this fucking government … You're fucking plebs.'"

Few people questioned the police version, or asked how it had become public property, while the press, including this paper, joined in the derision. Mitchell's position became increasingly difficult until he realised he had lost the support of Tory MPs and resigned on 19 October. It was not until December that the story began to unravel. In an outstanding piece of investigative journalism, Dispatches showed CCTV footage of the incident that made it highly likely the police account was a fabrication. Mitchell was not at the gate long enough, and there were almost no passers-by in Whitehall, certainly not the "several" who had supposedly been shocked by what they heard, and there was more to suggest graver forms of collusion or conspiracy.

What was dismaying were the prejudices revealed by this affair. A deplorable number of people – including journalists, who are meant to be natural sceptics – had been ready to believe a patently implausible story, because Mitchell is a well-heeled, expensively educated Tory, and because "it was the kind of thing he would have said".

No it wasn't. The kind of thing he was likely to have said was, "I thought you guys were supposed to fucking help us". That's what he admitted to having said, and apologised for saying. What he would not have said was that the police should learn their place, or that they were "plebs".

This is an old story. When there's constabulary duty to be done, and it includes fitting someone up by means of invented evidence, our bobbies have always displayed the proverbial cloth ear. The words attributed to Mitchell came straight out of the Jeffrey Archer school of dialogue. Or maybe the mind of the nation has been rotted by Downton Abbey.

A few of us, if I may say, recognised from the start that this was not a story about bullying cabinet ministers or Tory toffs but a story about the police. I shyly tried to explain that here, as did two former MPs in the Times. Chris Mullin of Labour reminded us that West Midlands was the force that had framed the Birmingham Six, and whose serious crime squad was disbanded after accusations of criminality. And the Tory Matthew Parris mentioned the part played by "that truly hideous organisation, the Police Federation". Another admirable piece of broadcast journalism, a Radio 4 documentary, claimed this hideous organisation had whipped up the mendacious story as part of its campaign against the government.

A belated investigation may reveal more of the truth and lead to prosecutions, though too late for Mitchell. But one good thing might come out of this disgraceful business. After decades of fawning on the police and truckling to the federation, our politicians might finally take a stand, and take them on.