In the months running up to this year's fateful general election, Peter Mandelson was the most formidable member of the cabinet. I witnessed him, at his peak as de facto deputy prime minister, trying to coax Gordon Brown and the rest of us to get off our ministerial chairs, take our noses out of our red boxes, and take Labour's fight to the people. "You should all be out there taking more risks to stir up controversy," he said repeatedly. "That's the only way to get media attention and expose the Tories." Although colleagues would nod in agreement, they rarely, if ever, followed his advice.

Mandelson and I were never natural buddies, but I found myself agreeing with virtually all his arguments in the political sessions of the cabinet that became increasingly frequent the nearer we drew to the election. His analysis of the Tories' vulnerabilities was masterful, as were the solutions and strategies he proposed. "We have the policies for the future, we have a past record to be proud of," he would say. "Now let's show some fight."

Yet it was as if he was trying to turn a lumbering carthorse into a surging stallion. Unlike me, most of my ministerial colleagues thought that we had already lost, and would say so in private. I, by contrast, had maintained for a while that the outcome of the election would be a hung parliament and that we had everything still to fight for.

Unfortunately, Mandelson's first ever, and much-deserved, standing ovation at last year's Labour conference will now be a distant memory. And that is because, at the very moment when there is real enthusiasm in the party to fight back, this book plays right into the media fiction, assiduously promoted by the Tories, that ours was a disastrous government. In case I didn't know it already, a visit last weekend to my South Wales constituency confirmed that most people who will never read the book in its entirety have already formed a firm opinion of it on the basis of a big-money newspaper serialisation. Predictably, this concentrated on a self- obsessed Labour glitterati apparently dazzled by power, wealth and glamour.

The Third Man contains enough gossip, intrigue and scandal to keep the cognoscenti titillated. But it also provides a powerful boost to political cynicism. Understandably, Labour Party members and MPs hate all this stuff. Party morale, even after our defeat, is astonishingly high and is combined with rising fury at the spectacle of the Liberal Democrats siding with the Tories in order to drive through savage spending cuts, at the same time gerrymandering parliament by fixing the Commons and packing the Lords. So, in Westminster, there has been a mixture of anger and sniggering at the author's tongue-in-cheek "Prince of Darkness" TV advert.

Anger because, although the book makes no great revelations (that there was a Blairite/ Brownite fault line in New Labour is hardly news), it is unacceptable to stir the pot as self-indulgently as Mandelson does, when the party is engaged in choosing a new leader and is desperate to make a fresh start. I can easily imagine his withering response to someone else doing the same thing, were he still in the leadership. (It should be acknowledged that Mandelson has served Labour with dedication and distinction. Indeed, according to the book, Gordon Brown, at a farewell gathering at party headquarters in London after he had resigned as prime minister, described him as the "rock upon which the stability of the Labour Party has been built for so many years". But the Machiavellian role in which he often appeared to revel has obscured his enormous talent.)

Mandelson agonises in The Third Man about the collective failure of the ruling triumvirate to which he belonged to stop the poison circulating between Blair and Brown and their camp followers. Having given birth to New Labour, they were also responsible for its demise - yet Mandelson keeps saying plaintively, "It should not have been like this!" He rather glosses over his own failings in this regard.

A key lesson of all this is that the party's next leader must junk all the factionalism that proved so corrosive of Labour's mission and vision. It was a big part of why we lost touch with millions of our natural supporters, as well as those whose votes we won in such numbers in 1997. As Ed Miliband has argued persuasively, more of the same will drive us into a cul-de-sac; but so will a lurch back to Old Labour. The new leadership must project a vision of bold but credible and authoritative change, and work to build a modern Labour Party rooted in the enduring values of social justice, greater equality and liberty.

For all the soap opera and psychodrama, there are valuable nuggets scattered throughout The Third Man. For example, in response to the recession, Mandelson developed an exciting strategy of "industrial activism", designed to support the new industries of the future. He writes tellingly: "That is the problem with government. No sooner have you worked out exactly what your policies are, pointed everyone in the right direction, and started to make them work, than it's somebody else's turn." Very true, but the problem with our government was that we should have had such a strategy in place from the very beginning, including Mandelson's first stint in the cabinet as secretary of state for trade and industry.

The best chapter comes last: "The End of New Labour?" is an insider's account of Labour's 2010 election campaign, in which he tried to fashion an effective campaign in the most unpromising circumstances. We had a brilliant but clumsy leader who had lost traction with the voters. In No 10, a talented team lacked clear direction because the man at the top did not facilitate it. And then there was the party itself, hollowed out and deeply in debt. Meanwhile, outside Westminster, civil society groups and trade unions were unwilling to mobilise in support of Labour after years of being shunned. As we sought a fourth term, following the worst global financial crisis since the 1930s, we faced a heavily resourced Tory party with the media in full cry behind it.

Mandelson is equally well placed to tell the absorbing story of the fruitless post-election discussions with Nick Clegg and his team. I was on the fringe of these negotiations, but his account confirms what I always thought: that although Clegg was certainly interested, he was never serious about coming to an arrangement with us. We were a means to striking a more favourable deal with David Cameron and the Conservatives.

For politicians, day-to-day arguments with colleagues can seem to take up all one's time, but they aren't the real story of government. If this book had concentrated less on the personal feuds and more on Mandelson's undoubted political skills, it would have been a far more fitting testament to a man who contributed so much to what was one of three great governments of the progressive left since 1900 - and which, in some ways, was the most successful of them all.

Peter Hain is MP for Neath. He was twice a member of cabinet between 2002 and 2010. His biography of Nelson Mandela will be published by Octopus in September.