Andy Burnham has a bubble ­complex. On Radio 4’s World at One on 29 May, he said: “Some voters have come to see Labour as a metropolitan elite inside the Westminster bubble.”

On the vexed issue of extracting oil and gas from shale rock, Burnham said on 5 June: “Fracking is one of those issues that gets politics a bad name. It is being driven ahead at speed by people in the Westminster bubble with scant regard for the views of the communities most affected. This is why people are fed up with politics as usual and want change. I will bring that change and put communities first again.”

In a speech in Crewe on 15 June, he said: “For too long, education policy . . . has been stuck inside the Westminster bubble, where the vast majority of people went to private schools and university.”

On the Murnaghan show on Sky News on 21 June, he said: “Labour’s been trapped in the Westminster bubble for far too long.”

On the same day, in an interview in the Mail on Sunday, choosing a different metaphor, he said: “Labour looks like an elitist Westminster think tank talking in language that people don’t understand.”

What is Andy Burnham trying to tell us? What he is trying to tell us, I think, is that this long-time political insider self-identifies as an outsider. His populist pitch for the leadership seems to amount to little more than that he’s a pretty regular kind of guy who – because he went to a comprehensive school, likes football and speaks with a northern accent – has an instinctive gift for communication and, as he would put it, can talk in a language that people understand.

But this is disingenuous. As with Ed Miliband or Ed Balls, Burnham is, in effect, a member of what George Osborne calls the “guild” of professional politicians. Practically his whole career has been spent in and around Whitehall and Westminster. After graduating with a degree in English from Fitzwilliam College, Cambridge, he worked as a researcher for Tessa Jowell, shared an office with James Purnell and played for New Labour’s Demon Eyes football team. One senior Labour MP remembers him back then as a “good Blairite boy”, eager to please and very ambitious. Like the Miliband brothers, he was fast-tracked into a safe seat and then the cabinet. If he has a gift, it is for staying out of trouble and sensing the direction of travel. Once a Blairite, he has now repositioned on the populist left of the party, becoming the self-declared champion of the public sector, having also assiduously wooed the big unions, which are supporting his leadership bid.

No one who has met him doubts Burnham’s self-belief or determination to lead the party – he also contested the leadership in 2010, when he finished fourth in a contest of five behind the feuding Miliband brothers and Balls. What is in doubt is his intellectual capacity and character: does he have the will and courage to challenge the party and move it on to what Jim Murphy, the outgoing head of Scottish Labour, called in a speech last week “the hardest ground”?

In 1976, after Harold Wilson resigned as prime minister, the six contenders to replace him were Roy Jenkins, Jim Callaghan, Anthony Crosland, Tony Benn, Denis Healey and Michael Foot. How Labour yearns for figures of comparable stature today. And yet, in retrospect, that contest signified the end of an era just as Gordon Brown’s defeat would in 2010: the country was entering a new period of Conservative rule as the free-market right launched a counter-hegemonic assault on the postwar economic consensus, dividing and then splitting the Labour Party along the way.

This time around, Labour is unlikely to split but the abject election defeat has left its MPs demoralised – there’s been much muttering to the effect that there might have to be a second contest in 2018 if the new leader is perceived to be failing. Problematic, too, is the fragmentation of the left, with Labour having lost so many votes to the SNP, the Greens and Ukip. Worse still, Labour looks to have been decisively defeated in Scotland, just as the Tories were before them. The party’s struggles are not happening in isolation but are part of a larger trend: throughout Europe the mainstream social-democratic left is losing power and influence, most recently in Denmark. In this context, Burnham’s complaints about the “Westminster bubble” seem parochial and banal.

In his new book, The Road to Character, the New York Times columnist David Brooks writes that he has “lived a life of vague moral aspiration – vaguely wanting to be good, vaguely wanting to serve some larger purpose, while vaguely lacking a concrete moral vocabulary”.

Something similar could be said of Burnham. He knows what he wants and wants to be but his message is vague in the extreme. He believes he is a good man and the right man to lead Labour – and, by implication, Great Britain, one of the most powerful and distinguished nations on earth. But it’s not enough simply to want to succeed. You must have a concrete moral vocabulary and something distinctive to say, a guiding principle beyond a personal ambition to lead.

Brooks also suggests that, in recent times, we have shifted from a culture of self-­effacement to one of self-promotion. This is the age of the “Big Me”. One struggles to think of a profession more narcissistic than politics. And there’s a warning here for Andy Burnham as he talks up his talents as a plain speaker and communicator. He is the front-runner, the People’s Andy. Yet the danger for him is that when you peel back the outer layers of cliché – the grumbling about a “metropolitan elite inside a Westminster bubble” – there doesn’t seem much to behold beyond the sight of a man with a loud voice saying it has to be me.

• Now read Anoosh Chakelian and Stephen Bush's interview with Andy Burnham.