Gordon Brown announced yesterday an inquiry into the Iraq war. It will begin work under Sir John Chilcot, a former civil servant, next month. To the derision of opposition MPs, it will take a year to report (so beyond the date of the next election) and will hear evidence in private. Scepticism is the right response, but not for the reasons advanced by Mr Brown's critics.

The military campaign to oust Saddam Hussein was intensely controversial and led to the deaths of 179 British servicemen. To scrutinise that decision is right and necessary. But two inquiries have already been held: Lord Butler's considered intelligence failings about Saddam's weapons of mass destruction; Lord Hutton's examined the circumstances of the death of David Kelly. The announcement of a third inquiry suggests cynicism by an embattled Prime Minister and sectarianism by opposition parties who want not so much a disinterested inquiry as an official admission of guilt.

There are many aspects of Britain's intervention in Iraq from which lessons must be learnt. These include the failure to establish security immediately after the fall of Saddam and to provide adequate equipment for British troops. But the establishment of the Chilcot inquiry is prompted not by practical military concerns so much as a preconception that the Iraq war was wrong.

Anticipating the inquiry, Nick Clegg, the Liberal Democrat leader, declared: “We are talking about the biggest foreign policy mistake since Suez.” The place to have that argument was, and remains, the floor of the House of Commons. To try to resolve the issue by repeated public inquiries is to supplant the prerogatives of an elected Government by quasi-judicial means. The intention to hold a further inquiry predates Labour's recent disasters. There is little doubt, however, that the timing has been tailored to bolster Mr Brown's weak position with querulous backbenchers. Downing Street has justifiably pointed to the independence of the members of the inquiry, which includes (excepting one crossbench peer) no politician. It has also stressed the inquiry's scope, covering the period shortly before 9/11 to the completion of the withdrawal of British forces from Basra next month.

It would admittedly be unlikely if so broadly conceived an exercise yielded no useful incremental information, if at high cost to the taxpayer. The arduousness of the brief requires long deliberation if the job is to be done well. Hearing evidence in private, which is not the same as keeping conclusions secret, is justifiable too. It may encourage greater candour by witnesses.

But the very expansiveness of the exercise undermines its rationale. Inquiries into military campaigns are valuable when they isolate identifiable weaknesses. The Franks report in 1983 considered the failures of intelligence about Argentine designs on the Falkland Islands. After the Boer War, the Esher Committee inquired into Britain's unpreparedness for deploying troops overseas, and recommended the establishment of a General Staff. Neither inquiry was an attempt to judge a political decision to go to war.

Tony Blair's Government took a decision on bad intelligence but also a prudent assumption about the intentions of an aggressive tyrant. Iraq is a better place for the removal of Saddam and the belated success of counterinsurgency operations. Whether that justifies the initial military intervention is a question beyond the competence of a public inquiry. At best there is diminishing value in persisting with this exercise till critics of the Iraq war are satisfied with the conclusion. At worst, it is an exercise in short-term political cynicism intended to buy off the war critics. The result will be to undermine the credibility of such inquiries and, ultimately, to satisfy no one.