The latest estimate of its cost is an astonishing £181.2m. Its value was already in question long before last week's damning revelation from Tony Blair's former chief of staff, Jonathan Powell, that it was an unnecessarily grand gesture to Republicans in Northern Ireland.

Sinn Fein had actually made clear that a simple apology from the British would have sufficed. It would certainly have been cheaper.

The Bloody Sunday Inquiry should be at the forefront of William Hague's mind as the Shadow Foreign Secretary pushes for a comprehensive review of the Iraq war.

Such an inquiry would inevitably dwarf the Bloody Sunday proceedings. It would involve the examination of events months, or perhaps even years, before the conflict as well as examining how the war – and the post-war reconstruction effort – were conducted.

The process would require evidence from numerous politicians and civil servants as well as military and intelligence personnel. The threat to countless reputations would no doubt lead to many interested parties demanding expensive legal representation, funded by the public purse.

In order to justify this monumental cost in time and money, there must be some prospect that the report produced by an Iraq war inquiry would tell the public something fundamental that voters do not already know.

Yet, the argument made in favour of an inquiry amounts to a vague claim that lessons need to be learned, but Britain and the US have been learning those painful lessons for five years. The scale of the loss of life among both Iraqis and troops from Britain, the US and elsewhere, has guaranteed that the war has already been subjected to unprecedented scrutiny and debate.

It is now known, for instance, that the intelligence suggesting Saddam Hussein was hiding weapons of mass destruction was mistaken. The legal basis for the war was a matter of dispute within the Government. The Armed Forces were not properly equipped for the war or their "peacetime" role. The planning for post-war Iraq was astonishingly limited and demonstrated little understanding of the tensions that Saddam's downfall would unleash.

As a result of this planning failure, countless blunders were made in the weeks and months following the conflict, not least the decision to disband the Iraqi Army. These are just some of the many lessons learned.

This understanding is not limited to those who have pored over the details. The British public is far better informed about the Iraq war than it has been about any previous conflict. Events in Iraq have not taken place over the horizon out of public sight. Thanks to modern media, they have been beamed into living rooms and splashed over newspaper front pages on a weekly and sometimes daily basis.

Undoubtedly, there are details that are not yet in the public domain. There will certainly be files in computers and cupboards in Whitehall that certain officials or politicians may prefer remain locked away.

An inquiry might expose these, prompting a degree of embarrassment and perhaps even a resignation, but such revelations will not fundamentally alter public understanding of these events.

The push for an Iraq war inquiry smacks of desperation on the part of both the Conservatives and the Liberal Democrats. The Tories have still not forgiven themselves for their unstinting support of the Government when it made the case for war, while the Liberal Democrats are desperate to breathe new life into an issue which, thanks to their principled stand, has earned them more public respect than any other matter.

It is as if both parties share the public's collective sense of disbelief that the Government did not suffer greater political consequences for making such a monumental blunder. Tony Blair certainly lost some of his authority, but he still saw out a decade in office.

If Iraq was ever going to swing a General Election, it was going to be in 2005. But, despite the strength of feeling over the war, the Liberal Democrats only gained 16 seats and lost another five to the Conservatives who had supported the Government.

Settling old political scores does not justify spending millions of pounds on an inquiry. Iraq remains an important issue, but the opposition parties should be holding Gordon Brown to account over current issues such as the Government's vagueness over the future of the 4,000 troops who remain in Basra.

Iraq will remain a scar on Britain's conscience for years to come. It will only heal if, at some point in the future, the country emerges from its dysfunctional state and prospers. Sadly, this outcome appears as far away as ever as Iraqi forces clash with militias in and around Basra.

An expensive inquiry will not tell the public anything substantially new about the war or make up for the mistakes of the past. Voters have passed their judgment on this undistinguished period of British history. The priority for politicians from all parties should be to ensure that the country does not make the same mistakes again.