Andreas Whittam Smith: Authenticity is a great asset in a leader. David Cameron lacks it

What is going wrong for the Prime Minister, David Cameron? His personal standing with the electorate has fallen precipitously, according to opinion polls. I found a small clue to what may be doing the damage in one of the pictures of world leaders attending a summit meeting at Camp David outside Washington last weekend. They had taken time out to watch the Chelsea/Bayern Munich football match.

The photographers had snapped Mr Cameron leaping to his feet with arms outstretched to celebrate Chelsea's winning goal. It was the football victory salute. What could be more natural? Chelsea had won the Champions League for the first time. Yet it reminded me of the mid-1980s when Mr Cameron was at school.

In those days, public schoolboys were desperate to lose their upper-class markings and meld into the rest of society. They adjusted their accents, they dressed as if they had been brought up on housing estates, and they became enthusiastic supporters of the most popular football clubs. It was from that period that Mr Cameron's "hug a hoodie" injunction was probably derived. All the same, it was an affectation, a false note if you like.

Was that Mr Cameron's problem, I wondered? For false notes are damaging in politics, just as authenticity is a great asset. The naturalness of Mr Cameron's fellow old Etonian, Boris Johnson, for instance, served him well in the recent London mayoral election.

In the same photograph was the new French president, François Hollande. In a sober suit with an open-necked shirt, he looked as if he had forgotten to pack any leisure clothes, but that is not why I mention him. Rather it is because of the way he handled himself in the nine days between winning the presidential election and his inauguration. He quickly showed a fuller understanding of his new role than Mr Cameron has done of his.

Mr Hollande's victory was announced on Sunday evening 6 May but he had to wait until 15 May to be sworn in. In that short period, he had much to do and he continued to operate from his campaign headquarters. But when he arrived at his office on the Monday morning after the result, his colleagues noticed that something had changed. The President-in-waiting immediately began to distance himself from them. Before election day, they had wandered in and out of their leader's office at will. They automatically used the intimate "tu" form of address rather than the more formal "vous". Now they had to wait to be summonsed, sometimes for 48 hours. And they began to wonder whether they should switch back to "vous".

What Mr Hollande was doing was establishing the dignity of the office that he was just about to hold. By dignity I do not mean the trappings of the presidency, the majordomos at the Élysée Palace in their white ties and tailcoats or the cavalry of the Republican Guard in their shining armour. I mean behaving with the dignity that is necessary if you are to embody the ideals and the hopes of the people who have elected you.

Mr Hollande's predecessor, Nicolas Sarkozy, on the other hand, did not understand the almost sacred nature of his office. And that was a factor in his electoral defeat. French people disliked his ostentatious celebrations of his own election victory when he took a party of rich friends to Fouquet's, a glitzy café-restaurant on the Champs Elysées. They were not comfortable with his holidays on the yachts of rich supporters. They disapproved of his attempts to place his 23-year-old son, Jean, into a top business job.

Perhaps more than anything, the French people hated the way Mr Sarkozy swore vulgarly at a member of the public who had said something disobliging at an agriculture show in Paris. This was not presidential. All of France, from the deepest countryside to the smart arrondissements of Paris, shared a sense of dismay.

Mr Cameron is making precisely the same mistake as Mr Sarkozy, though in quite a different way. It is not holidays and restaurants and nepotism. Rather it is everything we have learnt about his relations with the Murdoch family, who control 40 per cent of the British newspaper market. The attendance at their parties, the invitations to Chequers, the official country residence of British prime ministers, the riding of the police horse lent to Rebekah Brooks, the frequent text messages to her signed with the initials LOL, which he took to mean "lots of love", all of this sticks in the British public's craw.

It does so because of what we know – and the Prime Minister also knows – about the bad behaviour and habits of the Murdoch crew and their hangers-on. Some of them will shortly be answering charges in court. A prime minister with a sense of dignity would not have spent a minute in their company.

In this way, Mr Cameron has demeaned the office he holds. Yes, the prolonged recession is partly to blame for his loss of popularity. A 1950s predecessor, Harold Macmillan, gave a wise answer when asked by a journalist what is most likely to blow governments off course. "Events, my dear boy, events," he said. But in Mr Cameron's case, I argue that there is more to it than external events.

He started well. He appeared to be the epitome of a prime minister from the very moment he stepped over the threshold into 10 Downing Street. His appearance, the cut of his suits, his fluent phrase-making, even his courtesy, all contributed to this impression. After all, Mr Cameron was the 19th prime minister that his old school, Eton College, had produced. He seemed to be enjoying an inheritance that was always going to be his.

But undetected at first was his lack of any sense that people expect the monarch and the prime minister both to display the best British qualities. Mr Cameron's insensitivity cannot be repaired. Yesterday, for instance, in the House of Commons, during questions, he called Ed Balls, the Shadow Chancellor, a "muttering idiot". This is what you might call somebody during a row in a pub after a few beers. It comes close to Mr Sarkozy's flare-up at the agricultural show. The electorate sees this laddish behaviour. It doesn't like it. And it will remember it. The Prime Minister is setting himself up for Mr Sarkozy's fate.

a.whittamsmith@independent.co.uk