Today's protest against the education cuts was uplifting: students, staff and others from all over the country gathered in their thousands to walk the route between Embankment and Tate Britain, pausing to boo at Downing Street. The weather was bright and clear, and the mood decidedly upbeat. Staff, students and others marched together under banners from colleges all over the country, while drums and chants protesting at the fees rang out for miles. There were a sizable number of Lib Dems protesting against their own party's U-turn on fees, and a sit-in outside parliament – the peace protesters who reside there were happy to give the students a quick lesson in the true meaning of anarchy.

Numbers were massive too, with around 52,000 turning out – more than double the NUS's original estimate. Police helicopters circled above the crowds, as protesters carried giant vultures, carrots, coffins and effigies of Tory politicians. But media reports will inevitably focus on one thing, namely the spontaneous occupation of and protest in Tory HQ at 30 Millbank Tower. Aaron Porter, the NUS president, was quick to condemn the breakaway protesters, describing their actions as "despicable".

As I write, about 200 people have occupied the building, and bonfires burn outside. Some arrests have been made and eight people – protesters and police officers – have been injured. Protesters have broken windows and made their way on to the roof. Twitter reports indicate that some have taken a sofa from inside Millbank and put it outside, with the quite reasonable argument that "if we're going to be kettled we may as well be comfy".

Direct action this most certainly was, the kind writers such as John Pilger have recently been calling for. It is hard to see the violence as simply the wilfulness of a small minority – it is a genuine expression of frustration against the few who seem determined to make the future a miserable, small-minded and debt-filled place for the many.

The protest as a whole was extremely important, not just because of the large numbers it attracted, and shouldn't be understood simply in economic terms as a complaint against fees. It also represented the serious anger many feel about cuts to universities as they currently stand, and the ideological devastation of the education system if the coalition gets its way. It was a protest against the narrowing of horizons; a protest against Lib Dem hypocrisy; a protest against the increasingly utilitarian approach to human life that sees degrees as nothing but "investments" by individuals, and denies any link between education and the broader social good.

The protesters – students and others – who occupied Tory HQ will no doubt continue to be condemned in the days to come. But their anger is justified: the coalition government is ruining Britain for reasons of ideological perversity. The protests in France and Greece and the student occupations here, such as the recent takeover of Deptford Town Hall by Goldsmiths students on the day cuts were announced, are indicators of a new militancy. At this point, what have we got to lose?

The best moments on any protests are when there is a real feeling of common purpose and a recognition that we are all on the same side. This is the true meaning of "big society" – the very thing that the coalition seems set on destroying, despite its rhetoric. This protest – in both its peaceful and more violent dimensions – is a sign of a country unafraid to fight back, for the first time in a long time.