You may remember that I wrote that it was a shame there wasn't a recording of the exchange between Andrew Mitchell, the former Chief Whip, and the police at the gates of Downing Street.

I also wrote that the most damaging accusation was not the swearing but the alleged use of the word "pleb", and that some of Mr Mitchell's supporters thought it highly unlikely that he would have said it. I added that if the word wasn't used, the whole affair amounted to no more than a fairly understandable outburst of temper and noted in passing the Hillsborough revelations which had emerged just before this incident.

It's telling that the very people who were most vocal in their condemnation of both the Sun and the police for having misrepresented – indeed, fabricated – the events at Hillsborough were those who were quickest to believe exactly the same sources, operating in exactly the same way, when they told them that a Tory minister was hurling abuse at the police. And so "Plebgate" (I preferred "Gategate", but Plebgate was the name that stuck) cost Mr Mitchell his job, as I had argued it shouldn't.

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Now, mirabile dictu, it turns out that there is a fair bit of evidence besides the say-so of the parties involved in this altercation and, mirabilius, it seems overwhelmingly likely that Mr Mitchell's account of events was closer to the truth than that of the police, who were misleading about at least one thing, which was that there were several members of the public nearby (there weren't). Mirabilissime, there also turns out to be a recording of Mr Mitchell's subsequent encounter with members of the Police Federation, from which it is clear that their spokesman was at the very least economical with the truth when he emerged from the meeting, telling reporters the MP had refused to clarify what he had said, when in fact he had given a full account.

Of course, when I say this is wonderful, it's wonderful for Mr Mitchell. It's not quite so marvellous for the rest of us, since if there are some members of the police force, no matter how few, prepared to stitch up a Cabinet Minister, imagine what they could do to the general public.

In fact, in some ways Mr Mitchell was even worse off than a member of the public disputing the police's version of events. The average citizen may find that the courts value the police's word over his, but he can at least maintain that they are wrong. That option isn't really available to a politician; to claim that the police are lying would be politically disastrous.

It may yet prove that the conflicting accounts of the initial incident have an innocent explanation. One possibility is that the police officers misheard the Chief Whip; I can just conceive of the phrase "you're supposed to ****ing help us" – which Mr Mitchell admits saying and which, though certainly uncouth and ill-mannered, is not actually a piece of abuse levelled at a policeman – being misheard as "****ing plebs", which certainly would be a direct insult.

Every police officer knows, after all, that eyewitness accounts of the same event can vary quite startlingly, even when no-one has any malicious intent or any motive for lying. The CCTV footage certainly indicates that Mr Mitchell's account is more plausible than that of the police present, since there doesn't seem enough time for him to have said what was in the official log, nor does the body language suggest such an abusive exchange. But a misunderstanding, rather than a conspiracy against him, remains just possible.

That can't, however, be said of the email sent to John Randall, Mr Mitchell's deputy, by someone who claimed to be a member of the public who had overheard the exchange. If, as it is now alleged, it came from a serving police officer who was nowhere near Downing Street at the time, that is an extremely serious matter.

Nor can the Police Federation's dishonest account of their meeting with Mr Mitchell be excused. Like many other bodies representing those working in the public sector, such as the BMA or the Royal College of Nursing, the Police Federation tends to present its views as if they were a matter of disinterested judgment. When it objects to Government reorganisations of policing, it does so by arguing that the public will suffer or be endangered. That is understandable as a tactic, but it disguises the fact that the Police Federation is a trade union. And as such, its only real interest is the terms and conditions of its members, and not the general public.

There's nothing wrong with that, of course. Trades unions should be about getting their members a good deal. But it doesn't always coincide with a benefit for the wider public. It's worth remembering, for example, that the BMA was fiercely opposed to the introduction of the NHS.

Where there is a very serious danger is when the police use conscious deception to back the case for their political objectives. The Police Federation certainly made hay out of the reports of Mr Mitchell's outburst, and misled reporters about their meeting with him. The head of the Metropolitan Police Federation disgracefully claimed that it nullified the Prime Minister's statement of sympathy over the deaths of two police officers.

I would like to believe, still, that the vast majority of police officers would not dream of behaving in such a way. But if even a very tiny minority will tell lies solely in order to gain a moral and political advantage in a wrangle over their own terms of employment, it is very damning indeed. It's bad enough when doctors' and nurses' union officials try to characterise any healthcare reform, no matter how modest, as an assault on the NHS, or an attempt to privatise it, but such arguments can at least be seen as political rows, and the facts of the matter should be available for discussion and debate.

The police, by the very nature of their work, must have a scrupulous insistence on telling the truth, and a rigorous intolerance of any deviation from that standard. Very often in disputes between the police and others, we rely on the force itself to investigate the facts of the matter. The case of Mr Mitchell, and others such as Hillsborough and the killing of Jean Charles de Menezes, have seriously undermined the public's trust that they will do that honestly. That is a catastrophic failure.