Not the least extraordinary thing about the campaign to leave the European Union is that it turns out no-one was in charge of it. Things just happened and decisions were just made without the oversight or knowledge of the most senior politicians whose support for the project was reckoned, with some reason, to be crucial to its essential success.

If Boris Johnson gave the Leave campaign a popular - and populist - presence in the nation’s television studios, Michael Gove gave it a certain intellectual credibility amongst the - admittedly small - percentage of the electorate that worries about such things. And with good reason: Gove’s intelligence, if not always his judgement, has never been in doubt. He has been a reforming minister in every department in which he has served. In his current role at the department of the environment - a top ten job after Brexit, incidentally - he sometimes gives the impression of being almost the only cabinet minister with even half an idea about what to do after the great day of national liberation arrives. And certainly one of the very few who, in his department’s case correctly, views it as an opportunity.

But, really, it is possible to think this and to have a healthy admiration for Mr Gove while also thinking it's not good enough for Michael Gove to wash his hands of a campaign in which he played such a leading part. Perhaps you cannot win a referendum without breaking eggs but there is something galling about seeing a man who cheerfully broke so many eggs apologising for their destruction as though that meant their destruction didn’t really matter because it was just a ploy, a means of winning votes, but certainly not something that should have been taken quite so very seriously. Come on.

Yet here is Gove telling Tom Baldwin that he wishes the Leave campaign had not talked about the prospect of nearly 80 million Turks moving to Britain with quite the relish it did. It turns out that this made Gove uneasy and, perhaps, even mildly queasy. Asked by Baldwin if he regretted “appealing to some very low sentiments” during the campaign, Gove replied: “I know what you mean, yes. If it had been left entirely to me, the Leave campaign would have had a slightly different feel.”

But, forgive me, Gove was not just a foot soldier obeying orders. If he was not charged with running the day-to-day campaign he was still part of its high command. Now he says that “There is a sense at the back of my mind that we did not get everything absolutely right. It’s a difficult one.” Except it isn’t really.

Because even if Gove was not the strategy’s sole proprietor, he still delivered all the right - which is to say all the wrong - lines in public. So he had a choice. He could have said to his colleagues, ‘Hang on, this is all a bit strong and, you know, based on something which my colleague Mr Johnson said as recently as March is “not going to happen”’ or he could have said nothing and gone ahead and warned the British people that the imminent arrival of millions of Turks would break the National Health Service. Reader, he chose the latter course and you are entitled to remember that. Gove’s embarrassment laced, perhaps with a smidgen of something close to shame, seems a little too little rather too late.

The Vote Leave campaign, after all, told us that “David Cameron cannot be trusted on Turkey”. If you want Johnny Turk for a neighbour, vote Remain. This was hardly subtle; nor was it very different from the stuff peddled by Nigel Farage. If you lie down with Farage you can’t be entirely surprised if you are tainted by Farageism.

As Gove said a couple of weeks before the referendum: “With the terrorism threat that we face only growing, it is hard to see how it could possibly be in our security interests to open visa-free travel to 77 million Turkish citizens and to create a border-free zone from Iraq, Iran and Syria to the English channel”. Indeed so, which may be one of the many reasons why no-one was suggesting such a thing was likely or even plausible in any realistic appraisal of the medium, and for that matter, long-term.

It may be that one day Europe’s decision to turn its back on - or block, for sensible reasons - Turkey’s european aspirations will be seen as a strategic error. Be that as it may, Turkey’s chances of joining the EU are only slightly worse in 2018 than they were in 2016 when they were - as a man as intelligent and decent as Michael Gove must have appreciated - all but non-existent.

But the Turkey stuff was central to the Leave campaign. The combination of security concerns and the supposed threat to the NHS was political dynamite. Add the spectre of vast and uncontrolled and swarthy immigration and you had an issue even third-rate demagogues could do something with. If this meant lying then so be it.

To be clear, we all know that politics is a contact sport and that the rough and tumble cannot be entirely avoided. Perhaps it shouldn’t be either. Equally, we understand that the truth is often janus-faced and sometimes, even, something that can be bent without quite being broken. There is a difference, however, between that and scaremongering based on palpable lies that are known to be lies. (Some of Remain’s economic warnings came perilously close to this; the best that may be said of them is they were based on things that could happen whereas the Turkey stuff was built upon an entirely false prospectus that was known to be false by the people pushing it.)

And, again, Turkey was a big issue. We know this because the Leave campaign admitted it. In “All Out War”, Tim Shipman’s definitive account of the Brexit campaigns, According to Shipman, Dominic Cummings had a habit of ending meetings by saying “We want to win, therefore whatever we just talked about now, what we’re going to talk about in the campaign is 350 million quid, immigration, Turkey. And we’ll win”.

Shipman’s account notes that “Despite the furore, Vote Leave kept pushing the Turkey line. In Westminster Tower Cummings would walk past Richard Howell most evenings and ask, ‘What’s in the grid for next week, Ricardo?’ Howell would reply, ‘Next week is Turkey week, boss.’ The campaign director’s response would always be, ‘That’s right. Every week is Turkey week’. ‘Turkifying’ stories became a key goal for the research team.”

So this was not a massive secret and to be disquieted or mildly troubled by this was to be disconcerted by the Leave campaign itself. A campaign that, whatever the merits of its intellectual criticisms of the EU’s shortcomings, was at root based upon a brace of untruths: a cash bonanza for the NHS (now to be funded by taxation and borrowing) and the imminent reality of a Turkish takeover of Britain.

It has long been obvious that the real meaning of Brexit is this: They broke it, you own it. But while this may apply to the aftermath, I didn’t appreciate until now that the Leave campaign can’t or won’t even own its own campaign.

They ran a low, grubby, and dishonest campaign. They won. That’s fine. The result is the result. The least that can be demanded, however, is that they accept how and why they won and that senior people inside that campaign ceased trying to wash their hands of decisions and tactics for which they were wholly culpable. Own that at least.

None of this alters one other fact. It is true, as Gove has said on a number of occasions now, that the public mood on immigration has softened significantly since Brexit. Remainers should acknowledge this. It turns out that the idea of having control may be more important and more powerful than whatever you actually do with that control.

Be that as it may, the nature of the campaign - and not just the result - is one of the reasons post-referendum divisions have not healed. When leading Leavers all but apologise for the campaign they ran - for that is where intimations of regret must lead - they all but admit their prospectus, while effective, was deeply dishonest. That has consequences, few of them good, for all of our politics. It is a way of poisoning the political well. And the impact of that continues to be felt. I like Michael Gove and have a significant amount of admiration for him but on this issue, in this instance, it’s much too little much too late.