Andrew Grice: The Iraq inquiry has rebounded on Brown, but he has little to fear

The newspaper-style leaflets are going out across London, and will soon go nationwide. "Iraq cover-up shame" blasts the front-page headline. The photograph shows two men shaking hands: George W Bush and... Gordon Brown. True, Tony Blair is pictured separately, but Mr Brown is up there in neon lighting.

The leaflet has been produced by the Liberal Democrats, the only of the three main parties to oppose the 2003 war. It helps to explain the handbrake turn which will see Mr Brown give evidence to the Iraq inquiry before, rather than after, the general election.

The Liberal Democrats clearly hope that Blair-Brown will merge into one in the public mind. Although Labour's private polls suggest that most people still regard Iraq as "Blair's war", Mr Brown backed the invasion and, despite a few nods and winks to the contrary, said later he would have done the same. As Chancellor, he signed the cheques (some of them, anyway). Evidence at the inquiry has made clear he was in the tight "inner circle" Mr Blair consulted in the run-up to war.

Setting up the first over-arching inquiry into the conflict seemed a good idea at the time. It was seen in the Brown camp as part of his "not Blair" agenda after becoming prime minister in 2007. Some insiders believed he might get a little credit for it. Labour critics of the war saw the inquiry as the final part of a healing process only partially completed at the 2005 election.

Few Labour folk thought then that we would still be debating the Iraq war five years on as another election loomed. Today, Cabinet ministers wonder how Mr Brown has managed to allow Iraq back into the headlines in the run-up to the poll, offering the media an easy diversion from the less-than-convincing prospectus offered by the Conservative Party.

Ministers worry that the failure to find weapons of mass destruction in Iraq is a toxic symbol of Labour's mendacity, undermining the party's efforts to regain trust after the MPs' expenses saga and reinforcing the Tories' "time for change" message.

Labour strategists fret that the inquiry will remind many natural Labour supporters why they deserted the party in 2005. Labour is desperately hoping that the real prospect of a Tory government would lure them back into the fold this year. Some may now have second thoughts.

Mr Brown wanted the credit for calling the inquiry before the election, but didn't want damaging headlines until after it. He thought that could be achieved by having the report published after the election and the hearings behind closed doors, but had to beat a hasty retreat when a private inquiry became untenable.

The Prime Minister did not object last month when Sir John Chilcot, with all the caution of a retired Whitehall mandarin, suggested that he appear after polling day to keep politics out of the process. But 10 days ago, Nick Clegg cleverly demanded Mr Brown be held to account on Iraq before asking the voters to re-elect him. Knowing the issue was likely to be raised again at Prime Minister's Questions this week, Mr Brown took out an insurance policy: on Tuesday, he wrote to Sir John offering to appear "whenever you see fit".

Surprisingly, the inquiry team decided to take Mr Brown at his word and call him sooner rather than later. Sir John intended to announce its decision yesterday but told Downing Street on Thursday night and, to his consternation, the news leaked out minutes later, no doubt with a bit of help from No 10.

For Mr Brown, appearing before the election is now by far the lesser of two evils. Imagine the charges of "running scared" during the campaign – including in the leaders' three televised debates. The best hope for him is to face the music and get his inquiry appearance over with as soon as possible, in the hope that the image has faded a bit by May.

The Prime Minister will tell the hearing that invading Iraq was the right thing to do but admit that mistakes were made in failing to plan for the aftermath – America's department, not ours. Of course, it won't be easy and there will be difficult questions to answer.

Mr Brown would certainly not have started from here. Yet it might not be as bad as it looks. British elections are normally dominated by domestic events; Iraq in 2005 was an exception to the rule. This year, it's the economy, stupid – which, for all his faults, remains Mr Brown's strongest suit and best hope, as the end of the recession is formally announced next Tuesday.

David Cameron can't exploit Iraq; he supported the war, approved by the Commons thanks to Tory MPs, so he can't resile from it now.

The other ray of hope for Mr Brown is that his appearance before the inquiry will be eclipsed by Mr Blair's. For once, Mr Brown won't mind. There will be a frenzy when the former prime minister is questioned next Friday. Anti-war campaigners have already christened it "judgement day". But those hoping that the Chilcot inquiry will deliver Mr Blair's head on a platter or pave the way for a war crimes trial will be sorely disappointed.

All that doesn't alter the fact that the Iraq inquiry has boomeranged on Mr Brown, as a lot of his good ideas seem to do.