Joan Smith: John Prescott is the Princess Di of politics

The biographical details are eerily familiar: the childhood blighted by an acrimonious divorce, the failure to thrive at school, the crippling shyness made worse by press intrusion, even the bulimia. After almost a month of excruciatingly embarrassing revelations, I'm afraid there can no longer be any doubt. John Prescott is the Princess Diana of British politics.

The girl from a stately home and the boy who failed his eleven-plus both grew into adults who rushed from official functions to throw up. They railed against journalists, but were so desperate for attention that they were prepared to expose the most intimate details of their lives to public gaze. In another weird parallel, there were three people in Prescott's marriage, although he could hardly claim to be the wronged party in his affair with his diary secretary.

It's more complicated than you might think, this business of class. Growing up with wealth, titles and privilege doesn't guarantee happiness or even a modest degree of contentment, any more than living in a council house condemns you to lifelong misery. Of course Prescott didn't get a decent education as a boy but he made up for it later by going to Ruskin, which is more than poor Diana, with her prize for hamster-keeping, ever managed.

I'm sure the comparison with the Princess would horrify the former deputy prime minister, bearing in mind his admission last month that he was embarrassed to admit to an eating disorder because he associated it with teenage girls. But his sense of martyrdom, given another airing yesterday on BBC Radio 4's On the Ropes, puts him in the same class (in this sense at least) as the late Princess. They've both joined that category of celebrity open only to people who are willing to turn themselves into public property, and Prescott may find it as much a trap as Diana eventually did.

Like her, he loathes journalists but has co-operated with one to get his version of events into the public domain; like her, he seems to believe that he's a hapless victim rather than in control of his own life. Yes, he told John Humphrys yesterday, the affair with Tracey Temple was entirely his fault – but a moment later it was "just one of those things that does happen". Like catching a cold, I suppose, or missing a train?

You would never imagine from his account that he happened to be the second most powerful man in the country at the time. Even when he tried to hang on to Dorneywood, the grace-and-favour residence in Buckinghamshire where he was famously photographed playing croquet in 2006, he said he wasn't doing it for himself: his wife Pauline would be "devastated" if he had to give up the mansion, he told Tony Blair.

It seems clear that Prescott has an internal narrative in which he figures as the long-suffering protagonist of a life packed with setbacks, slights and betrayals. In that sense his book, Prezza: My Story, due out this week, is a faithful portrait of his inner world, even though he isn't even clear about his role in its production. He enjoyed writing it, he blithely said earlier this week, only to perform an immediate volte-face: "Well, I had a ghostwriter, mind, I wouldn't have enjoyed it if I'd had to write the damn thing."

It isn't snobbish to suggest that someone who has held one of the highest positions of state should be unequivocal about whether or not he wrote his autobiography. But Prescott's performance on On the Ropes was a reminder of his longstanding touchiness and inability to handle criticism; even in response to perfectly reasonable questions, he reacted by talking over Humphrys in a loud, sneering voice.

It's as if Prescott believes the fact that he failed his eleven-plus, and was later the victim of cheap Tory jibes about his job as a ship's steward when he entered the Commons, has given him carte blanche to be as rude as he likes to anyone he perceives as an opponent – and that seems to be most of the world, from Tory MPs to the "beautiful people" in his own party.

In the past, his blokeishness has revealed itself in his willingness to use his fists, and he is even more of an old-fashioned class warrior than Cherie Blair, whose newly-published autobiography reveals her own obsession with her origins. But Prescott's working-class background isn't the whole story, any more than Cherie Blair's account of growing up in Liverpool as the daughter of an impoverished single mother tells you everything you need to know about her.

They are both hugely successful people, placed by their political convictions and connections at the heart of a Labour government which effectively wiped out the Tories – the party of inherited wealth and privilege – for a decade. And the real mystery is why they, as much if not more so than their critics, are so obsessed with where they came from rather than what they have achieved.

Cherie Blair's admission that she got pregnant on a trip to Balmoral because she did not want the royal servants to unpack her contraceptive equipment has received a great deal of ribald attention. The point of the anecdote, however, is what it says about a woman who is not just uncomfortable with servants – many of us on the left feel the same about the whole nonsense of hierarchy and deference – but afraid of what they might think of her. This is inverted snobbery, suggesting that the then Prime Minister's wife is still at heart a working-class girl terrified of bringing shame on her family.

Although John Prescott is older than Cherie Blair, they are both beneficiaries of the social mobility which characterised the post-war period. So am I, and I never thought that growing up in a succession of council houses would hold me back; I'm not ashamed of my working-class background but I'm not obsessed by it either. And I can't help thinking that banging on about class is sometimes a cover for other anxieties, too painful to be confronted, such as the childhood disruptions which can affect people of any background.

Lady Diana Spencer watched her mother leave home when she was six, prior to a divorce in which her maternal grandmother sided with her father. Cherie Booth (as she then was) lived with her grand-parents for two years after she was born, going to live with her parents not long before they separated. John Prescott's parents fought bitterly and divorced, exposing him a dreadful conflict of loyalties. Such people are often high-achievers in later life, craving the limelight and feeling impelled to tell their side of the story.

Whether they get much satisfaction from it in the long run is doubtful, and the recent spate of memoirs has certainly done no favours to the Labour Party. But the worst damage is self-inflicted; John Prescott cannot complain if he goes down in history as the most self-pitying public figure ever to hold high office.