The long-awaited Chilcot inquiry into the Iraq war will not be published until after the general election in May, it has emerged.

The inquiry chairman, Sir John Chilcot, will set out his reasons for the further delay in an exchange of letters with Prime Minister David Cameron tomorrow, according to Government sources.

The inquiry was originally set up by the then prime minister Gordon Brown in 2009 and took public evidence from its last witness in 2011.

It is understood that Mr Cameron has written to Sir John saying that while he would have liked to have seen the report released before the election in May, he accepted that publication was a matter for the inquiry.

Earlier this month at Prime Minister's Questions, Mr Cameron spoke of his "immense frustration" at the continuing delays.

The disclosure that it will not now happen before polling day comes as MPs prepared to stage a Commons debate next week on the hold-ups.

Senior Tory backbencher David Davis, who was the driving force behind the staging of the debate, said that it was "incomprehensible" that it would have to wait until the next parliament.

"Frankly this is not good enough. It is more than five years since it started," he said.

"We need to know why. This is not simply some formality. This is for the whole country to understand why we made a terrible mistake in Iraq. Simply putting it off is not good enough.

"Why has this taken so long? What is going on that is preventing this? The report was created in the first place by a Labour government in order to get an understanding of what went wrong. I can think of no reason why this should be deferred."

Angus Robertson, SNP Westminster Leader, said: "If Chilcot is to be delayed again that would be an absolute scandal . It is now more than five years since Chilcot stopped hearing evidence on the illegal invasion of Iraq and it should be published without any further delay and certainly before the election."

It became increasingly clear that the report was unlikely to be made public before the election after ministers disclosed last year that it would have to be released before the end of February if it was not to interfere in the electoral process.

Publication has been held up by wrangling over the release of confidential messages between Tony Blair and former US president George Bush and the so-called "Maxwellisation" process by which people who are criticised in the report are given the chance to respond.

Sir John finally accepted an agreement whereby he would publish the "gist" of the communications between Mr Blair and Mr Bush after the Cabinet Secretary Sir Jeremy Heywood blocked the publication of the full exchanges.

However, the protracted dispute - and the need to declassify thousands of official papers - further delayed the start of the Maxwellisation process, putting back the eventual publication date.

Critics have pointed the finger at Mr Blair - who is widely expected to be criticised in the report for seeking to slow down the process - a claim the former prime minister has strongly rejected.