Matthew Norman: Cameron's biggest test has arrived. Is he up to the job?

If he wasn't quite George W Bush when interrupted with the 9/11 news while reading The Pet Goat to second graders at a Sarasota elementary school, there was still a hint of trauma in the Prime Minister's eyes when he spoke yesterday morning outside No 10. Then again, you need not have been recalled from Tuscany for a venomous Cobra meeting to be scrambled and punchy. Which of us isn't?

Whatever happened in London and elsewhere last night, or preferably didn't happen, this has not begun to sink in. Anarchy in the UK is too bewildering in itself and its implications to be blithely computed. It is also too surreal. Watching fire engulfing that Croydon mattress store on Monday night, watching that young man, injured in Barking, having his rucksack insouciantly picked in the midst of it, as if in a modern-dress reworking of Oliver Twist, watching the police watching looters in the guise of mildly interested observers, it wasn't like watching real life at all. It felt more like a post-apocalyptic cable mini-series, a cheap and shoddy piece of cataclysm-porn in which what some glib politico calls "the very fabric of society" has been incinerated, leaving feral youth to battle mutant rats for control of the streets.

The questions smash into one another as if in a motorway pile-up. As indeed it is. For the Afro-Caribbean community, for a few retailers and homeowners, for the Met, for the political class, for us all, this is one monumental car crash. How it happened, how the Met screwed up yet again, why Mr Cameron and Boris Johnson took so long to come home and countless other questions race to mind. Those are the easy ones, and the first of them will take years to answer. Regardless of yesterday's fatuous declaration that this is "criminality pure and simple", the Prime Minister knows otherwise.

The grandest question, meanwhile, is this. Is David Cameron fit for purpose? Does he have the brains, temperament, nerve and resilience to rise to a challenge the like of which few peace-time leaders, if any, have faced – that of salvaging a country no longer fit for purpose itself?

He and his Coalition are under twin attack, and the assailants are connected. This is not to suggest, like the egregious Ken Livingstone, any direct causal link between the spending cuts and the rioting, any more than between the Tottenham shooting and the mayhem in Ealing. But the connection between the disasters in finance and looting extends beyond their shared terminology of fire-fighting and contagion. With both, catastrophe narrowly averted without the structural flaws addressed means catastrophe postponed. Put out the sovereign debt inferno in Greece and it resurfaces in Italy. Send coppers to douse the rioting in Camden Town, and it spreads within the hour to Chalk Farm.

There was a time, as I said, when David Cameron understood that you cannot cure mortal illness by treating the symptoms. But it's easy to be wise in opposition, as he was five years ago when he gave the "hug a hoodie" speech, which is worth a brief revisit for its prescience. "Imagine you are 14 years old, and you live in a flat four storeys up. It's the summer holidays and you don't have any pocket money. That's your life. What will you get up to today? Go to a football game? No – you're talking £30 or £50." Well, you might be if the friendly against Holland hadn't been cancelled. "So what do you do? You hang around in the streets, and you are bored, bored, bored. And you look around you. Who isn't bored? Who isn't hanging around because they don't have any money? Who has the cars, the clothes, the power?" Since he is the one with the power, he needs to recall his own words. There is nothing simple about the combination of forces – greed, poisonous disrespect for others, scorn for authority born of nihilistic hopelessness, adolescent adrenaline – that drives the young to anarchy. This is not to offer a looters' charter.

Excusing the crime would stretch bleeding- heart liberalism into facetious imbecility. Yet if the flames are doused with 16,000 police on London's streets while their causes are ignored, how much more destructive might they be when they resurface in a year or two once the cuts have started to bite? In the midst of a mortifying present, the British instinct is to seek nostalgic refuge in the past. So hats off to Radio 4 Extra for choosing 1 am yesterday morning, with the street contagion spreading, to broadcast Dixon of Dock Green. "A spate of bicycle thefts makes Andy desperate," ran the synopsis for "Crawford's First Pinch", adapted from a 1955 TV episode, "to notch up his first arrest."

David Cameron appears as out of his time and place as PC Crawford would have done had he been transported from Dock Green to the streets of Clapham. More than ever, the PM looks like a patrician one-nation Tory who has slipped through a tear in space-time, and emerged blinking and bamboozled from his comfy berth in the Fifties' Old Etonian "magic circle" of Eden and Macmillan.

The nagging sense of a clever, well-intentioned man betrayed by a charmed life of quarantine from urban realities has never nagged so violently. Fiddling about on holiday near Rome while London burned was a terrible, terrible mistake. It reinforced the impression of a leader cocooned by naivety and its kissing cousin privilege, as he was over phone-hacking, from the nasteries of modern life.

One of those nasteries has spoken eloquently for itself at all corners of the capital, and in cities to the north. Another – a disenfranchised underclass that treats authority with the same contempt it lavishes on empty rhetoric about the need to work for a future it knows does not exist – will take longer to correct. Yet somehow he must address both at once. If the immediate crowd control measures seem understandably desperate, desperate times and all that. But the PM also looks desperate. Desperately slow to react, desperately short of gravitas, and desperately remote from the admittedly unprecedented amalgam of pressures pincering him today. A premiership already wobbling from the Coulson fiasco and all the U-turns hangs on how he responds. Is David Cameron up to the job? No one, least of all himself, has a clue.

But his Hurricane Katrina moment has arrived, and we are about to find out.