The five candidates in Labour's leadership election agree on one thing: the need to "move on" from the backbiting, infighting and psychodrama of the Blair-Brown era.

Their desire to do so has been enhanced by this week's publication of Peter Mandelson's memoirs, which display New Labour's pettiness, jealousies and rivalries in inglorious technicolour.

Without irony, Lord Mandelson tells us he could not tell his story without describing "the occasional soap-opera aspects" of the relationship between the Three Musketeers – Mr Blair, Mr Brown and himself. Occasional? This soap opera ran daily from 1994, when Mr Blair overtook the long-time front-runner Mr Brown to become Labour leader. The final episode was in May when Mr Brown left Downing Street, becoming the "tail-end Charlie" he feared would be his destiny from the moment he decided not to run in 1994.

With all the nastiness, plots and destabilisation, it is a miracle that Labour got anything done in office, let alone that it won three general elections. Mr Brown managed to be Britain's most powerful Chancellor while devoting the other half of his brain to scheming how to prise Mr Blair out of No 10.

Mr Blair somehow governed the country while looking over both shoulders for a Brownite knife and, in his later years, stringing his Chancellor along, pretending he was ready to hand over power when he intended to carry on and hoping another successor would emerge. Lord Mandelson rather skates over this and it will be interesting to see whether Mr Blair admits, in his own autobiography in September, that he did not want his Chancellor to succeed him.

Somehow, New Labour kept the show on the road. Often by issuing 24-carat denials when people like me wrote stories about the latest Blair-Brown row or split. Lord Mandelson has already had plenty of flak from within the Labour camp for writing The Third Man. No doubt he was partly motivated by money and had a few scores to settle. But, among all the blood and guts, there is an important message to his own party which it ignores at its peril.

Labour's policies will inevitably change and, hopefully, the new generation will manage to avoid the vicious personality battles of the past 16 years. At least the party is having a proper leadership contest this time and the winner will have a mandate. Lord Mandelson, desperate to avoid a TB versus GB showdown in 1994, now admits it should have happened because Mr Brown felt cheated out of the prize. In 2007, Mr Brown ran a leadership campaign against ... well, no one but himself. Mad.

But a mandate to do what? The five candidates deliberately avoid the fundamental question in British politics – how to cut the £155bn public deficit. They do not want to alienate those whose party votes they seek, arguing that they can seek the votes of the electorate later.

If anything, Labour sends a signal to the public that it is going backwards. Ed Balls, the shadow Education Secretary, said this week that Labour's election pledge to halve the deficit in four years was "a mistake", adding: "I don't think it could have been done." Alistair Darling, whose pre-election battle with Mr Brown over the need for cuts is a fascinating part of the Mandelson memoirs, insists his strategy could have been delivered. But some Treasury officials doubt that a re-elected Brown government would have had the stomach for cuts of 20 per cent across the board.

Labour thinks it can now leave the dirty work to the Tories and the Liberal Democrats. It is wrong. "Fight the cuts" is a tempting slogan for the Opposition. But, as the Blairite shadow Business Secretary Pat McFadden told the Fabian Society on Wednesday, Labour can't wish the deficit problem away.

"People will still want to know what we would do differently," he argued. "The Tories and Lib Dems ... want Labour to retreat to its comfort zone and allow them to say that they alone are capable of facing up to Britain's problems." He said the choice for Britain was not simply the "echo of Thatcherism" offered by the coalition or "denial".

Similarly, Lord Mandelson fears his party is in danger of slipping back into the "either/or" mentality which pre-dated New Labour, which sees markets as all bad and government actions all good. He hopes his book will remind the new generation that the right strategy is the "politics of and", which means finding new ways to harness the private sector to deliver public services – and cut the deficit.

It might be music to the ears of the coalition as departments deliver their options for cuts of up to 40 per cent to the Treasury this weekend. But it is not a tune that Labour wants to hear.

Like it or not, the Labour leader elected on 25 September will have to listen. Of course the party needs to "move on" from the Blair-Brown era; it went on long enough. And yet the next leader will find that many of the dilemmas and tough choices that were faced by New Labour remain exactly the same – not least, how to live in the real world in order to regain power rather than settle into the comfort zone of opposition.