David Miliband is "waiting for his brother Ed to fail" as Labour leader and is "poised" to make another bid for the job, friends of the former foreign secretary revealed last night.

The extraordinary disclosure exposes the extent of the division between the Miliband brothers, which threatens to overshadow Labour Party politics for the next decade in an echo of the long-running enmity between Tony Blair and Gordon Brown. The image of brothers at war is underlined by the first biography of the Labour leader, which begins a newspaper serialisation today.

Ed Miliband, who pipped his brother to the post last September, is faced with growing discontent from Labour MPs over his failure to set out a clear strategy and narrative. Dissent has been heightened by an unsteady performance at Prime Minister's Questions last week, when David Cameron should have been on the back foot over NHS reforms and sentencing.

A poll in The Sunday Times today shows more than two in five Labour supporters believe electing Ed Miliband was the wrong decision. The paper also claims "big beasts", including Lord Prescott and David Blunkett, are beginning to express unease about his performance.

In a further blow, the head of Britain's biggest public sector union, Dave Prentis, who backed Ed Miliband in the contest, rounded on the Labour leadership for failing to stand up for the NHS. In an interview with The Independent on Sunday, the Unison general secretary suggested the Labour leader can no longer count on his union's automatic support when he said he still has "a lot to get right" and should abandon the strategy of only issuing "reasonable statements".

Last night, a friend of David Miliband told The IoS that relations are very poor, and that the MP was still hungry for the top job. David Miliband has turned down offers of several posts under his brother, leaving the impression that he wanted to retreat from frontline politics.

But the friend said: "David definitely wants it still. He is waiting for Ed to fail. He thinks the coalition will go the full term, so Ed has plenty of time to fail." There is no suggestion of David Miliband's planning a direct challenge to his brother, but his aides are mobilising in the expectation of his brother losing the party's support.

The Mail on Sunday, which is serialising the biography, Ed: The Milibands and the Making of a Labour Leader, claims David Miliband effectively accuses his 'ruthless' younger brother of lying about the way he stole the Labour crown from him.

The book, by James Macintyre and Mehdi Hasan, also claims David is scathing about his brother's performance, and that he thinks Ed is "heading in the wrong direction". The brothers are said to speak rarely, communicating mainly through officials. However, an aide to Ed Miliband yesterday insisted: "They talk regularly. They talked before, during and after the leadership contest. They are brothers first and politicians second."

There was discomfort among Ed allies when the speech David Miliband would have made to the party, had he won, was leaked to The Guardian, in what was described as a "highly provocative act" by Labour insiders. The leak, an apparent attempt to show MPs what "might have been", seemed to come from someone close to the former foreign secretary.

In his IoS interview Mr Prentis, whose union has given more than £800,000 to Labour since Ed Miliband took the helm, said the Shadow Cabinet "still believe they are in government and therefore have got to make reasonable statements".

He went on: "They are not playing their part strongly in opposition, which is what we'd want to do – hone in on what the Tories are doing and show the deficiencies in it." Mr Prentis said Labour had only "belatedly" begun standing up for the NHS against the threat posed by government reforms. "We were running that campaign for six months before we heard anything from the Labour Party."

Mr Prentis also revealed that he has a £30m war chest for "enormous" industrial action involving all 1.4 million Unison members in schools, hospitals and councils this autumn.

Ed Miliband will attempt to change the political weather with a speech tomorrow promising a different approach on welfare reform and calling for a "new era of responsibility" across British society.