Can this week's violent protests in Westminster simply be dismissed as the hijacking of an orderly demonstration by a 'small minory' of anarchists. Or are they a sign of things to come for an 'out-of-touch' government with 18 millionaires in its cabinet?

On and on it went: aerial shots of the heaving crowd, rolling commentary, bursts of stuff shot on mobile phones, and the usual parade of talking heads. While what the BBC was calling a "mini-riot" happened both inside and outside the Millbank tower, the people in charge of its news channel were presumably ecstatic: this kind of stuff, after all, is what rolling news was invented for.

Over there: a fire! Suddenly, on the roof: more protesters! On the phones: frantic office workers, taken aback by the disruption of their day! And in the midst of it all: that delicate and ever-shifting line of police, anxiously trying to do whatever they could, knowing full well that the people they were up against had already – if you'll excuse the pun – stolen a march on them.

Meanwhile, the president of the National Union of Students did the media rounds. Aaron Porter is 25; he stood for the office as an independent, but is a member of the Labour party, whose dress code – the Nick Robinson-esque glasses are a good example – rather suggests that he's destined for a career in mainstream politics. Certainly, if you fancy being a high-ranking Labour MP, clambering to the top of the NUS isn't a bad move at all. His predecessors have included Jack Straw, Charles Clarke, the current shadow defence secretary Jim Murphy, and Phil Woolas, the MP last week suspended from office for making misleading claims in the course of the last election campaign – all of which highlights the fact that NUS presidents are not exactly renowned for being what the French call enragés.

And so it proved. "Let me be clear," he told yet another camera. "I absolutely condemn the actions of a small minority who have used violent means to hijack the protest . . . if some people think it's appropriate to use violence, it's a total disgrace, and they have completely hijacked this opportunity to make a serious point." In his own way, he was endorsing the view that was subsequently splashed over the front page of yesterday's Daily Mail: "Anarchists spark violence as 50,000 take to streets over student fees – HIJACKING OF A VERY MIDDLE CLASS PROTEST".

On the BBC, there was a particularly priceless moment. When Porter once again talked about "hijacking", the coverage cut to the mass of people outside Tory HQ, the presenter made the point that this was not what "a small minority" would look like – and Porter seemed momentarily lost for words. You had only to look at the crowd to know that the vast majority of them were not anarchists, but reasonably regular twentysomethings. As if to illustrate the point, when one of the people on the roof made the stupid decision to hurl down a fire extinguisher">stupid decision to hurl down a fire extinguisher, they were met with an outraged chant of "Don't throw shit! Don't throw shit!"

Long after the fires had burned out, and the riot police had belatedly arrived, I spoke to a Guardian colleague who had spent most of Wednesday at the scene. Talk of cynical provocateurs, he said, was "nonsense": the crowd was made up of "ordinary students who were viscerally angry", but also mindful of what was ill-advised, or plain daft. When one of their number had prised up a cobblestone and moved to lob it at the police, he had been roundly told to "stop being an idiot"; moreover, the attempted occupation of Millbank had seemingly started on a whim, when a handful of people had walked into the foyer, not quite believing they had been allowed to do so, and decided to stay put. He was also unimpressed by talk of an assembly of self-indulgent, bourgeois moaners: time and again, he said, he had bumped into people from such northern towns as Bradford and Wakefield, who were students at FE colleges, angered to the point of fury by the government's axing of the educational maintenance allowance – the means-tested benefit that has enabled so many people to take up post-16 education without being a drain on the family budget.

His basic point – and mine – is simple enough. What happened on Wednesday afternoon was not some meaningless rent-a-mob flare-up, nor an easily-ignored howl of indignation from some of society's more privileged citizens. It was an early sign of people growing anxious and restless, and what a government pledged to such drastic plans should increasingly expect.

If you hadn't noticed already, these are strange, tumultuous times. We are still in the midst of the uneasy period of phoney war before the cuts actually bite, but we now know what's coming: the deepest and quickest reductions in public spending since the 1920s – which, according to an under-reported quote from David Cameron, will not be reversed, even when our economic circumstances improve (2 August, at an event in Birmingham: "Should we cut things now and go back later and try and restore them later? I think we should be trying to avoid that approach").

The welfare state is in for an unprecedented reinvention, as ministers get dangerously close to reviving the nasty old trope of the undeserving poor; yesterday, as if to try to neutralise recent fretful noises from the Archbishop of Canterbury, Iain Duncan Smith talked about supposedly self-imposed worklessness as a "sin". Changes to housing benefit look likely to drastically change the social makeup of our cities, and London in particular; even Boris Johnson has talked about the danger of "social cleansing".

Meanwhile, just about every area of our lives will soon feel the pinch: travel anywhere in the country, pick up the local paper, and it's all there – the imminent hacking back of youth centres, social care, school buildings, libraries, parks . . . you name it. Everyone will be affected: as ever, the most vulnerable will take the biggest hit, though it is no accident that the idea of the "squeezed middle" is being talked about as never before.

Of late, my mind has returned time and again to a celebrated article from 1999 by the Oxford academic Ross McKibbin, and one passage in particular: "The middle classes make more use of the NHS, public transport, public libraries, local swimming pools, public parks and their right to state welfare than anyone else."

Underneath the coalition's plans, there is an obvious enough agenda: not just the brutal cutting of public spending, but a decisive rolling-out of the market-obsessed, "choice"-fixated ideas that took root while Margaret Thatcher was prime minister, were revived and retooled once Tony Blair decided he had to define himself against the Labour party – and now look set to be taken to their logical conclusion by the Tories, and the like-minded Lib Dems who took their party into the coalition. Here lies another reason why Wednesday's events were so significant – for within the government's plans for higher education lie not just the hiking-up of fees, but an entire reinvention of the very ethos of our universities, whereby the idea of education as a public good takes yet another kicking, and everything comes down to "choice", and whatever is meant to be good for business.

A recent issue of the London Review of Books featured an inspired demolition of the Browne review, the report into higher education by the former chief executive of BP that was hailed by the government as setting its "strategic direction", and thereby opened the way for the lifting of the cap on fees, and much more besides. The LRB piece was written by a Cambridge don named Stefan Collini, and it quickly got to the heart of the problem: "Overwhelmingly, the general statements announce, with startling confidence, the real point of higher education: 'Higher education matters because it drives innovation and economic transformation. Higher education helps to produce economic growth, which in turn contributes to national prosperity.' . . . This report displays no real interest in universities as places of education; they are conceived of simply as engines of economic prosperity and as agencies for equipping future employees to earn higher salaries."

Meanwhile, where are the public? When it comes to tuition fees, do not believe the voices who tell us that the average Briton thinks students are a pampered lot who should get with the government's plans and count themselves lucky. A recent YouGov survey commissioned by the Sun found that the public opposed the Browne proposals by 45% to 37%; an ICM poll from around the same time offered the choice between raised fees and the far fairer option of a graduate tax, and found that people favoured the latter over the former by 61% to 29%.

More generally, presumably to the delight of the government, a cliche has long since oozed into the reporting of what they are up to: that people accept the need for drastic austerity, and are meekly preparing for the necessary dose of fiscal medicine. Browse the requisite opinion polls, and you could be forgiven for assuming the worst: late last month, for example, Ipsos Mori found that 59% of people agreed that there was "a need to cut public spending on public services" – the kind of statistic cited almost daily by those newspapers who habitually encourage the government to go further, and faster.

In fact, things aren't as simple as that. According to the same poll, the share of people who think the government has made either the right or wrong calls on public spending is evenly split: 41% and 38% respectively, while one in five simply don't know; 40% of people disagree with the idea that the coalition's approach will improve the state of the economy; while 49% reject the idea that, as the coalition insists, public services will somehow improve in the long run; 47% oppose cutting back the number of people who work in the public sector. Public opinion, it seems, is as contorted and contradictory as ever – and for the government, there is much less comfort than you might imagine.

While the coalition comes over all Churchillian, endlessly talking about the "national interest" and the spurious idea that we are "all in this together", there is also a low hubbub of noise about their shortage of a mandate. On Wednesday, the ire of the marchers was focused on all those Lib Dems who blithely signed the NUS's anti-fees pledge ("I pledge to vote against any increase in fees in the next parliament and to pressure the government to introduce a fairer alternative" – yesterday, Nick Clegg limply said that he "should have been more careful" than to put his name to it). But there are also serious questions about the Tories – not just that they are pushing what Cameron recently called a "revolution" with the support of around one in five of the electorate, but also when it comes to the pronouncements they made during the election campaign.

Consider, for example, a now-infamous quote from the PM, issued on the Andrew Marr show on 2 May: "What I can tell you is any cabinet minister, if I win the election, who comes to me and says: 'Here are my plans' and they involve frontline reductions – they'll be sent straight back to their department to go away and think again." And really: they wonder why some people are increasingly angry.

And so to the wider context, and things that most of the media very rarely mentions. Political debate in Britain is endlessly distorted by the way that London so dominates the national conversation, and assumptions that run wide and deep in some of Britain's more desirable postcodes are assumed to blur into the national mood. In Islington, Notting Hill, and the more upmarket corners of the home counties, austerity will doubtless be taken in a lot of people's stride: if you have opted out of large swaths of the public sector and earn a six-figure salary, the prospect of the cuts will inevitably cause you relatively little worry. Self-evidently, this will not be the case in Bolton, Merthyr Tydfil, or Hastings; but neither will it hold true in Basildon, Crawley, or Harrogate.

At the top of government, what might be called the "experience gap" grows even wider. There are at least 18 millionaires in the cabinet: Cameron is said to be worth around £3.4m; Nick Clegg's wealth is put at a mere £1.8m. Of late, even commentators on the right have been talking about the distance between some ministers and the people at the sharp end of their policies, not least when it comes to the middle class. Last month, for example, the Daily Telegraph's Peter Oborne bemoaned their "devastating" fate, in a piece worth quoting at reasonable length, if only to prove that the idea of an out-of-touch elite blithely wreaking havoc is not the preserve of hard-bitten lefties.

Among Oborne's most telling passages was this one: "Doubtless both David Cameron and George Osborne think of themselves, quite genuinely, as middle class. Indeed, a few weeks ago, David Cameron referred to himself as a member of the "sharp-elbowed middle class", and the political intention of this remark was clear: he was claiming associate membership of the club of hard-working people who pay their taxes, do their best to rear their children and find it desperately hard to make ends meet. Few would challenge the Camerons' fundamental decency. But the middle-class people David and Samantha Cameron know socially tend to be on quarter of a million a year and upwards. Life for them may indeed be tough, but only in the sense of whether they can afford a skiing holiday or a spring break in the Caribbean."

In last week's news that Cameron had put his personal photographer on the public payroll, there was a slight touch of the Marie Antoinettes, and a tension that may yet cause the government no end of trouble. It boils down to this: if you are secure in such an exclusive social bracket, it will inevitably distort your view of things. Around £27,000 for a university degree may well seem like the acme of both affordability and common sense; lost child benefit may seem like money dropped down the back of the couch; people on welfare will inevitably look like the residents of a completely different planet.

Meanwhile, some longstanding assumptions seem to be changing at speed. Wednesday gave the lie to the idea that our young people are thoroughly post-ideological creatures, with no fight in them; if even the most fusty newspapers are worried about the chasm that separates the government from the so-called squeezed middle, you can bet that the politics of class may yet make an unexpected comeback.

Oh, and one other thing. Though few people seemed to notice, on 3 November, a Treasury minister named Lord Sassoon served notice that the coalition's work on City bonuses was done: "The government has taken action to tackle unacceptable bonuses in the banking sector," he said, and that seemed to be that. Six days later, Barclays announced that its latest bonus pot would total £1.6bn – which is about a third of what the government currently spends each year on university teaching. The annual season of big executive payouts is about to commence once again; at this rate, do not be surprised if the seditious spirit of Millbank spreads – and fast.