Why did they get it so wrong? That is the fundamental question Lord Butler should address in his report.
The claim that Saddam Hussein had weapons of mass destruction was central to the dossier the government published in the autumn of 2002 prior to the vote in Parliament which authorised the prime minister to send British troops to invade Iraq.
That dossier was, as the prime minister insisted, "in large part the work of the intelligence services". Supervising its drafting was John Scarlett, then chairman of the Joint Intelligence Committee (JIC), and a former senior officer in M16.
His document may well have been crucial in persuading many members of Parliament to vote for the war. Yet its central claim was wrong.
The error of thinking that Saddam had a WMD arsenal is described on BBC Panorama by Michael Herman, a former Secretary to the JIC as "the biggest failure of intelligence since the failure to predict the German offensive in the Ardennes at the end of 1944".
Lord Butler's report will be published on Wednesday
Even Tony Blair now admits Saddam's weapons of mass destruction may never be found.
In their defence, Britain's intelligence services will no doubt have insisted to Lord Butler that Saddam acted like a dictator who had weapons of mass destruction and was trying to hide them.
After all, he had used them against Iran and against the Kurds; he had obstructed the UN inspection teams; and he'd been caught lying when Iraqi officials had said they'd never had a biological weapons programme - just as one was being identified.
I doubt, however, that Lord Butler will be satisfied with that defence. The claim made by the intelligence dossier was that Saddam could deploy chemical and biological weapons within 45 minutes.
An assertion as specific as that must have been based on more than general suppositions derived from Saddam's past record.
And yet, as Lord Butler will have discovered, the raw material on which the JIC based the 45 minute claim turns out to have been astonishingly thin: there were no details about the location of the weapons, or their size, or whether the warheads were actually chemical or biological, or whether they were battlefield shells or ballistic missiles.
A further surprising aspect of the 45 minute claim is that up until the autumn of 2002, the JIC was unwilling to pronounce unequivocally on whether or not Saddam still possessed any weapons of mass destruction at all.
Dr Brian Jones, then the British intelligence establishment's top analyst on the topic, thought that there was "an absence of any firm intelligence" on Iraq's production of chemical weapons.
Interestingly, before the autumn of 2002, the JIC had broadly shared Dr Jones' expert assessment. The claim in the spring of 2002 that Saddam "may have retained some chemical and biological agents and munitions" from before the 1990 Gulf War was as far as the JIC was willing to go.
And even then, JIC emphasised that it could not say whether the dangerous agents in the munitions were still effective. Lord Butler's report will reveal what led the JIC to change its view so radically.
John Scarlett, who was promoted by the prime minister earlier this year to the post of head of MI6, has explained that MI6 received new intelligence from Iraq on 11 September 2002. That was precisely the moment when the notorious dossier was being prepared.
The first draft of the dossier had already been criticised by one of the prime minister's advisers as "intelligence lite".
The front page of the government's Iraq dossier
The new intelligence conveniently arrived the same day that the JIC put out "a last call" for more items of intelligence to strengthen the dossier's claims on Saddam's weapons of mass destruction, because "No 10 ... want the document to be as strong as possible within the bounds of available intelligence".
The following day, the JIC's chief drafter was on the telephone to Number 10 offering to come over to ask the press office if they were on the right track.
Sir Richard Dearlove, then chief of MI6, went personally to the prime minister to announce the arrival of what is believed to be the same intelligence which was corroboration for Saddam's "recent production of chemical and biological weapons agents".
Sir Richard personally attested to its credibility, saying that it could be used to underpin assertions in the dossier - but also insisting there could be no specific references to it.
The new intelligence was so secret it was not even shown to the intelligence services' own experts - analysts such as Dr Jones - never mind assessed by them.
It was, however, used to support the dossier's central claim: that Saddam had weapons of mass destruction that he could launch within 45 minutes.
Yet, aside from the 45 minutes report, Sir Richard's new intelligence seems to have been substantially all that had changed since the previous spring to support the claim that Saddam had any workable weapons of mass destruction at all.
As we all now know, the new intelligence turned out not to be reliable: it was false. I have been told that it has recently been formally withdrawn by MI6.
That incident illustrates how difficult it will be for Lord Butler to avoid the conclusion that the JIC in general, and Sir Richard and John Scarlett in particular, were too ready to accommodate the prime minister that, consciously or not, they adapted their judgements to fit his beliefs.
Tony Blair was personally convinced that Saddam continued to possess weapons of mass destruction. Lord Butler may find, however, that what little reliable intelligence there was on Iraq simply did not support that view.
The reliable intelligence did not even support the view that Saddam represented a threat to Britain. Tony Blair insisted, in the foreword to the dossier, that he believed Iraq was a serious and current threat.
Right up to the last moment, the drafts of the dossier were thought by No 10 to do "nothing to demonstrate a threat, let alone an imminent threat, from Saddam. It does not demonstrate he has the motive to attack his neighbours, let alone the west".
Scarlett obligingly redrafted a passage in the dossier so that it clearly implied that Saddam posed a threat - at least to his neighbours.
Scarlett said he did it because he had found some "quite clear evidence" to support it. Lord Butler may find that his decision to rewrite passages of the dossier had more to do with the fact that the spooks got bewitched by the glamour of being part of the tiny circle around Tony Blair taking all key policy decisions on Iraq - and tailored their judgements accordingly.
MOD weapons expert Dr Brian Jones said there was an absence of firm intelligence on Iraq's WMDs
In his public statements the prime minister asserted that Saddam was a threat because he might link up with terrorist groups such as al-Qaeda and pass on his weapons of mass destruction, or the know-how to build them.
Two months after the publication of the dossier, the JIC came to the conclusion that there was no intelligence to indicate that Iraq had considered using chemical and biological agents in terrorist attacks.
That fact was not, however, disclosed to Parliament or public - despite Mr Blair's promise when he announced the publication of the intelligence dossier to facilitate the "fullest possible debate...as the situation develops".
Sir Andrew Turnbull, as cabinet secretary, was perhaps in the best position to explain to Mr Blair that he ought to take a more even-handed approach in his publication of intelligence, given that it was not evidence but judgement and assessment and therefore inherently risky.
However, Sir Andrew's visibility during the dossier episode seems to have been very low. Lord Butler, a previous occupant of the job, may be extremely critical of this.
Michael Herman, a former secretary to the JIC, quotes approvingly that "interested policy makers quickly learn that intelligence can used the way a drunk uses a lamp post - for support rather than illumination".
Lord Butler, in more measured, mandarin language, may conclude that this is what happened in the case of the Iraq dossier - with Blair as the drunk, and the JIC as his lamp post.
Panorama: A failure of intelligence was broadcast on BBC One on Sunday, 11 July 2004 at 22:15 BST