I'm late for my interview with David Miliband. "What time do you call this?" asks the shadow foreign secretary with a grin as he appears at the door of his office, a banana in hand. Pity there wasn't a photographer around.

Miliband is in jovial mood, joking with his aides. He has a good deal to be pleased about: the MP for South Shields and former cabinet minister has been the undisputed front-runner in the race for the Labour leadership since it began on 12 May. So far, he has more support among MPs, trade unions and constituency parties than any of the other four candidates. And in the first month of the contest he amassed, according to the Electoral Commission, £185,265 in donations from major backers - more than six times as much as his nearest rival (Ed Balls raised £28,419).

But, endorsements and donations aside, what sets him apart from the other candidates? Miliband leans back in his chair. "I think I'm the leader who can fire the imagination of the public as well as the party, unite the different talents of the party and be a credible prime minister." "Credible" is a word often associated with the shadow foreign secretary. He has the highest-level experience of the five MPs vying for the top job - having served in the cabinet as environment secretary and then foreign secretary - and is perhaps the most intellectual, if not intelligent, person running for the leadership.

The elder son of the late Marxist thinker Ralph Miliband, and a graduate of Oxford University and the Massachusetts Institute of Technology, he worked as an analyst for the Institute for Public Policy Research before serving as head of Tony Blair's policy unit in Downing Street and writing the 1997, 2001 and 2005 general election manifestos. "He likes writing manifestos," jokes an aide.

He may be the biological son of a Marxist, but he has long been considered the political heir to Blair. The latter is said to be backing the shadow foreign secretary's leadership bid privately, as are other members of the Blair inner circle, including Alastair Campbell, Andrew Adonis and Peter Mandelson. Because of these personal and political ties, and his enthusiasm for public-sector reform, Miliband is often described as a Blairite. His allies, however, argue that the label is too crude. For example, it doesn't take account of Miliband's opposition to the Israeli invasion of Lebanon in 2006, or his role as secretary to the Commission on Social Justice, the body set up in 1992 by John Smith whose deliberations eventually led to Labour's introduction of the minimum wage. Indeed, it has been suggested that he was prompted to leave his job as head of the Downing Street Policy Unit and stand for parliament in 2001 because Blair did not consider him sufficiently "reformist". And so far in this campaign, Miliband has distanced himself from New Labour by adopting a series of left-wing policies: abolishing charitable status for private schools; extending the tax on bankers' bonuses; supporting the introduction of a mansion tax on £2m houses and a so-called Robin Hood tax on financial transactions.

Nonetheless, as one of his shadow cabinet allies tells me, "David is struggling to get the balance right between the importance of both defending the [New Labour] record and admitting to the mistakes and errors of the past." So how does Miliband respond to those who call him a Blairite? "They're probably not saying that to boost my chances of winning this leadership election," he says, with a laugh.

As he says this, I can't help noticing that he shares so many of Blair's mannerisms, not to mention his style of speech and even his height. "Look, my position is very simple," he continues. "The best of New Labour represents the best of the Labour Party." But what about the Blairite label itself? "I've said before I'm a Milibandite." It is perhaps not the most distinctive label to choose, given that there are two Milibandites in the race.

The elder Miliband's relationship with his brother, Ed, has dominated the media coverage of the Labour leadership election. The pair were the first brothers to serve together in cabinet since Austen and Neville Chamberlain in 1929, and are now the first brothers in history to run against each other for the leadership of a major political party. Can brotherly love survive an intense and highly personal battle for the top job? Surely, he must be annoyed with his younger sibling for running? He won't say, but he does concede that he "wasn't really surprised" when Ed decided to stand. Thereafter he is reluctant to discuss his brother any further.

Would he serve in a shadow cabinet under Ed? Or any of the other candidates, for that matter? Friends of the shadow foreign secretary have suggested he might retire from front-bench politics if his campaign to become leader is unsuccessful. Miliband shakes his head. "I'm not walking away from the people of South Shields. I'm not walking away from the Labour Party." But what about his future, specifically on the front bench? "I'm very happy to serve under anyone."

A common criticism of the five leadership candidates, both in Westminster and among party activists, is that they have failed to articulate a new social-democratic vision for a Labour Party tasting opposition for the first time in 13 years. Miliband, however, has arguably gone further than the rest in laying out his beliefs and offering an analysis of the root causes of Labour's defeat. In his Keir Hardie Lecture in South Wales on 9 July, Miliband accused Gordon Brown of having failed to renew Labour in office and meet the government's need for "greater moral seriousness and less indifference to the excesses of a celebrity-drenched culture". He called on the party to "reconceive our notion of fairness" and to "build our own story of political economy that embraces neither the masochism of George Osborne nor a denial of economic reality".

But couldn't any of the five candidates have delivered such a speech? Miliband says his lecture was "a distinctive set of propositions", but adds: "That's not to say that there aren't individual parts of it that different people would sign up to."

The lecture has nonetheless given his campaign an intellectual and ideological boost. The influential backbencher Jon Cruddas, who is on the left of the parliamentary party and whom some consider to be a "kingmaker", described it as "the most important speech by a Labour politician for many years".

There is one thing, however, for which sections of the left will never forgive Miliband - as a junior minister, he supported the invasion of Iraq in March 2003 and, as foreign secretary, continued to defend the government's subsequent record on Iraq. During this year's general election campaign, Miliband told anti-war voters that they had "punished us enough about Iraq", and his position has not shifted in opposition - unlike his brother and Ed Balls, neither of whom opposed the war at the time but who have, since the leadership contest began, noisily distanced themselves from it.

Does he not worry that his own campaign is hamstrung by his refusal to disown his vote for the invasion? "If we're going to fight this leadership election - or effectively mortgage the next general election - on Iraq, then I think we're making a grave mistake," Miliband says, irritated. "If the only candidate you can vote for is someone who resigned or made clear their opposition to Iraq in 2003, then Diane [Abbott] is your woman." In an obvious dig at the two Eds, he adds: "What I'm not willing to do is rewrite history."

Indeed, Miliband seems to believe that his refusal to budge on Iraq, or disown a war that he says he supported "in good faith", could bolster his credentials as a man of principle and integrity. "I think that people will have to make up their mind if they can trust someone who sticks to their position as clearly as I have," he says, but then qualifies this, noting: "I'm not saying that I was right about the WMDs. Evidently, I wasn't right about the WMDs."

I point out that there are countless former Labour voters, such as my own father, who abandoned the party over Iraq and can never bring themselves to vote for Miliband, no matter how much they might admire his intellect, his eloquence or his domestic policies. What does he say to them? "Why cut off our noses to spite our face?" he says, gesticulating vigorously. "Why say, if you think there is one guy who is most likely to stop an appalling government from doing terrible things to the country, that we're going to miss the opportunity to try to get rid of the government?" He then pulls out a pen and starts writing a letter to my father. "What's your dad's name?" It's Riaz. "Can I say 'Dear Riaz'?" He scribbles a short note to my father, on headed paper, and gives it to an aide to post.

Miliband has been described as a "combination of alpha male and nerd", and throughout the interview he speaks with authority and precision. But can he lead his party back into government? "Labour has a historic responsibility . . . most of the time when we lose, we end up losing for a very long time," he says. "We need to buck the historical trend. That is going to take huge acts of will, imagination and effort on behalf of the whole party, not just the leader."

As the interview draws to a close, I ask him what phrase or idea he would want Lab­our under his leadership to be associated with. "Fairness," he says, but then pauses and checks himself. "Actually, I think fairness sounds a bit glib now and is sort of used too much." Another pause. "The one thing would be the equal worth of every individual, because that is a far more radical notion than people realise. If you take seriously the idea of equal worth, you do far more to tackle inequality of opportunity, to build mutuality and reciprocity . . ."

Before I leave, Miliband says that he could have gone off to have "one of the biggest jobs in world politics six months ago: to be the EU high representative for foreign affairs", but he chose to stay instead and fight on behalf of the party he loves. If, against the odds, he loses this leadership election and ends up serving under one of his four rivals - not least, his younger brother - he may spend the rest of his life regretting that decision.

The questionnaire

If you weren't a politician, what would you be?
Teacher.

What's your favourite meal?
Fish and chips from Colmans of South Shields.

What does God mean to you?
Something that gives other people enormous strength.

Have you ever taken drugs?
No.

What is your most valuable possession?
My photo of my wife and children.

What would you consider your biggest fault or character flaw?
Agreeing to answer surveys.

Who would you advise your supporters to give their second preference to?
Well, I'm not going to advise them. But in this contest there's only one other candidate that I can honestly say I love.