WHERE governments are concerned, accidents and coincidences are not to be trusted. This doesn't mean they never happen. It doesn't mean we should surrender to every conspiracy theory passed off as fact thanks to the internet's Chinese whispers. But scepticism, plenty of it, never goes amiss when a government department is making excuses.

A lot of us are prepared to believe almost anything now about powerful individuals and the abuse of children. It isn't irrational. We know, too late, where doubt and disbelief have led us. Rumours dismissed for years have turned out to be terrifyingly true. Victims have been tortured twice, first by their attackers, then by an officialdom refusing, honestly or otherwise, to listen.

What do we say, then, to Whitehall's strange ability to lose and find files that might relate to abuse? That such is the complexity of government? That mistakes happen? That back in the olden days – say, less than 30 years ago – civil servants simply failed to understand the issues at stake? That somehow things are no better now? In each case, a remarkable degree of naivety would be involved.

We would have to have a high degree of tolerance, too, for sheer incompetence. That possibility might not test credulity too much. Government officials have shown a remarkable ability to lose their laptops, or leave their briefcases in taxi cabs. But the idea that officialdom cannot lay hands on its records, that it is in such a perpetual mess it cannot even vouch for the existence of files, invites derision. All you have to decide is who is being mocked.

But there we have it. Let's say there is an official review, by Peter Wanless of the NSPCC and the barrister Richard Whittam, of allegations that in the 1980s the Home Office covered up the abuse of children by politicians. Let's say that after the pair have investigated the department's own supposed investigations – fruitless, it seems – into the whereabouts of 114 missing files, we hear that neither culpability nor innocence has been established.

Theresa May, the Home Secretary, then admits that a cover-up “might” have happened, but this is the best she can offer. For his part, Wanless says it is impossible – thanks to sloppy Home Office record-keeping – to reach a “categorical conclusion” on whether incriminating files were destroyed. It's most unsatisfactory, all agree, but “nothing specific” has been found. MI5, searching its own files, has found nothing “relevant”. We, the public, have to be satisfied with that.

Wanless and Whittam published their review last November. Suddenly the Scottish not-proven verdict was enjoying unusual popularity in Whitehall. Then, earlier this year, two senior civil servants from two departments – the Cabinet Office and the Home Office – wrote to Wanless, each admitting, all of a sudden, that there had been a “flaw” in earlier responses and searches. Then, as though by magic, more documents popped into existence. You have a choice of responses: either, “That's lucky”, or “Are they serious?”

Last week, in a newly-published appendix to their report, Wanless and Whittam stuck by their conclusions. However, they also stated: “We are concerned and disappointed that the Cabinet Office was aware of the separate Cabinet Office store of assorted and unstructured papers yet informed us that the searches covered all records and files held.” In the case of the Home Office, the pair simply called for a “broader search” by Justice Goddard and her independent inquiry into child sex abuse.

Even by Whitehall's standards, this is a brazen display. Did the Home Office forget that it had papers stored at the National Archives in Kew, or just forget to ask for them? Is it customary for potentially sensitive papers to be “unregistered”, or is that just the first step in ensuring that documents are “mislaid”? The same question would apply to the Cabinet Office and its “assorted and unstructured” papers. Is it believable, in fact, that no-one within the entire machinery of government had any memory of these documents?

In their appendix,Wanless and Whittam come close to accusing the Cabinet Office of dishonesty. They certainly assert, with remarkable understatement, that it “is essential that the public have confidence in the searches that were undertaken, not least because we had to rely on the efficiency and integrity of those who sought material on our behalf. The emergence of these papers only after our review had completed is not helpful in that regard”. You could, of course, say that again.

Whitehall will not be too dismayed. Wanless and Whittam were allowed very little time to begin with. A pursed-lips appendix to a half-forgotten report that came to no firm conclusions will seem like a result to those who specialise in obfuscation. It resembles a sinister version of Yes, Minister. Such is mandarin stupidity, however, it is liable to have the opposite effect – at least in this observer – to the one intended. Trust, such as it ever was, crumbles a little more. And the list of questions grows longer.

There's one in particular. This particular Whitehall farce has taken us nowhere nearer to understanding contemporary opinions on the behaviour of politicians such as Leon Brittan, Thatcher’s parliamentary private secretary, Sir Peter Morrison, the former diplomat Sir Peter Hayman, and the former minister Sir William van Straubenzee. All of these Tories are dead. The paperwork in which they are mentioned will be passed to the Goddard inquiry. But where's the investigation – yes, another, if needs be – into the treatment of files?

Is “Didn't think to look there” now an adequate response from a senior civil servant? If that is not credible, or is actually incredible, where are the consequences for the officials and departments involved? If the allegation is one of cover-up, why accept the excuse of error and accept, implicitly, that the whole affair is, in that favourite euphemism, “historic”? Given what Wanless and Whittam have disclosed, it should now be for Whitehall to prove that a cover-up is not still going on, government after government.

Set against the feeble excuse of sloppy file-keeping, the supposition does not qualify as paranoia. After all, these disclosures come just as we are told by Theresa Villiers, the Northern Ireland Secretary, that files relating to the Kincora boys' home scandal need not concern Justice Goddard. She is content with Stormont's inquiry, established under the retired judge Sir Anthony Hart, because it is “doing an exceptionally good job”.

Digest that. After all, a central allegation arising from the hellish Kincora affair, one that has persisted for decades, is that the security services knew all about the abuse (at the very least) and used the information to blackmail the rapists. The claim could not be more serious. But as Villiers knows perfectly well, Hart has no power, none whatever, to compel members of the security services to give evidence.

A banana republic would do better. It would certainly put on a better pretence. The largest lie of all is that relentless secrecy is the means by which the British state keeps us safe. Clearly, obviously, the state keeps its secrets to protect its own. But you won't find that in the files.