It must be the most famous slip of the tongue in Westminster's recent history. Just before Christmas in 2008, Gordon Brown stood up at prime minister's questions and stumbled through a defence of his rescue of the banks that came out as "We not only saved the world …", before being drowned out by derision from the MPs opposite.

Cue Lord of the Flies-style baiting from David Cameron's Tories. Cue insta-comment from the pundits who, just three months after Lehman's collapse, were already ravenous for normal Commons fare. Yet Brown's mis-statement wasn't so wide of the mark. Despite the mocking, and the political obituaries that marked his historic defeat at the general election, the evidence suggests that the last Labour prime minister is in with at least half a shout of keeping the world economy afloat in 2008-2009, and an excellent claim of having saved the UK.

Not that you'll get to hear much about the actual evidence elsewhere.

Commentators routinely wrap up the son of the manse's entire record in government as "the Brown Terror" (Jeff Randall); write him off as "unreliable and dishonest" (the economist Tim Congdon); or simply "a terrible prime minister" (Andrew Rawnsley). Some of these criticisms are justified; others are just barking, like that bloke who still yawps away on the Spectator website about the sale of the gold reserves in 1999.

Out of power, Brown doesn't have many public defenders left. The careerists have scarpered, and the man himself is almost invisible. Not for him the usual New Labour afterlife: Blair's mysterious Faith Foundation or David Miliband's habit of writing articles for the New Statesman so banally opaque that the only question they prompt is "what did he think he meant by that?"

But if we correct the account of those two years, it not only makes for fairer history; it recasts some of the biggest current political controversies. Labour politicians might at last be able to qualify the story that all their government did was leave the country a massive overdraft – that amid the biggest crisis since the 30s, they made largely the right calls while the Tories got it largely wrong. Even more important, it could open up the stiflingly narrow debate over how Britain should respond to a looming second recession.

So cast your mind back to the weeks and months after Lehman went down. Financial markets were freezing up. The world economy was going into cardiac arrest. In Britain, there was a very real prospect on some nights that cash machines wouldn't open in the morning.

What sticks out about that period is how Brown and Alistair Darling were not only acting without a roadmap, they were driving with Cameron and Osborne right on their bumper telling them to do a U-turn. The diagnosis that British banks were dangerously low on capital was correct – but it was the opposite of what most bankers were saying.

The decision to put government money into stricken banks was exactly the policy that Bush and his treasury secretary Hank Paulson had pooh-poohed. In the end, however, the US and others copied the British plans. As Nobel laureate Paul Krugman remarked: "Brown and Alistair Darling have defined the character of the worldwide rescue effort, with other wealthy nations playing catch-up." And how Brown was sneered at for cajoling other governments to pump money into the world economy. How the Tories leapt upon Germany's denunciation of his policies as "crass Keynesianism" – then kept mum when Angela Merkel launched her own massive budget stimulus. The $1tn deal brokered by the British government at the G20 summit in 2009 was described by the World Bank as "having broken the fall" of the global economy.

None of this is to deny Brown's own role in presiding over the boom that led to a bust. Or to forget his relative slowness to tumble to the seriousness of the crisis in the summer of 2008 (then again, so was Mervyn King – and he still got a knighthood). It is simply to observe that when the moment of maximum danger came, Brown had the right diagnosis and did largely the right things. This is as close as contemporary, otherwise Lilliputian, politics comes to heroism.

The same goes for that most controversial of Brown's policies as prime minister – to offset a global recession by cutting taxes and creating jobs for young people. That decision has never got the credit it deserves. As the former Bank of England policy-maker Danny Blanchflower notes in the most recent New Statesman, the budget stimulus led to Britain's economy actually growing 3.1% between the autumns of 2009 and 2010. Under the coalition in the year afterwards, it grew 0.3%.

We can argue over the details of the Brown bailout, but the big lesson is: governments can stem mass joblessness and banking crises. It's a lesson the Tory anti-statists just don't want to learn, and that Labour is now too diffident to make. Economists widely expect a double-dip recession this year, and yet Osborne and Cameron prefer to tinker with red tape. It's safe to say that this prime minister would never make the mistake of claiming to save the world; but he's already made the much bigger error of sitting on his hands.