Thursday lunch time at the City of London headquarters of Royal Bank of Scotland (RBS), and at the stroke of one o'clock, 200 people arrive on the pavement outside. Some are wearing red nooses around their necks, others are parading around in top hats and City-boy pinstripes, a few are carrying placards that read, "Storm the banks". A pedal-powered sound system is cranked up and The Fall's anthem to grinding poverty, "F'oldin' Money", blares out across the street.

This is a flash-mob demonstration, mobilised through a Facebook event called "Give us our money back". It's a protest against the Government pouring billions of pounds into the banking industry and the £16.9m pension pot awarded to the former RBS chief executive Sir Fred Goodwin. A man picks up a megaphone. "Congratulations, people," he says. "After the biggest bailout from the poor to the rich that this country has ever seen, this bank now belongs to us. The time has come to claim what is rightfully ours." The protesters applaud wildly. "Whose money?" they chant over and over, "Our money."

Armoured police vehicles are scattered up and down Bishopsgate and the grand glass-fronted entrance to the RBS building is guarded by a phalanx of the Met's finest. From within, a few bemused RBS workers look nervously out at the street. It's probably not the best day to be slipping out for a boozy banker's lunch.

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Standing cackling on the sidelines is Ian Bone, a self- confessed "lifelong enemy of the state" and member of the Whitechapel Anarchist Group (WAG). "This is just a taste of things to come," he says. "That was the spring offensive. Next up is the summer of rage." Bone is referring to a wave of mass demonstrations planned for the capital which kicked off yesterday with the Put People First march, organised by a coalition of trade unions and environmentalists. On Wednesday, 1 April – or "Financial Fools Day" – thousands more are due to take to the streets of the City for the biggest show of public anger since the credit crunch began. And Thursday, dubbed G20 Meltdown, is when protesters will descend on the Excel Centre in London's Docklands – the day that world leaders arrive in the capital for the G20 summit.

According to media reports, police are gearing up to deal with unprecedented numbers of protesters and terrifying levels of violence. Fears are also growing for the safety of City financial workers. The G20 Meltdown campaign posters show a besuited mannequin being hanged. City staff are being advised to dress down and cancel all non-essential meetings.

"People are in an incendiary mood," says Bone. "1 April will see the biggest ructions on the street since the poll-tax riots and possibly even the Gordon riots of 1780. I don't think politicians realise quite how angry we are. In the past six months, this country has been turned upside-down. A deep recession has been created by a few greedy bankers and as a result, thousands have lost their homes and jobs. A dam of resentment has built up and 1 April is when all these pissed-off people march on the City to take what's theirs. Capitalism itself is on the ropes."

Bone believes the anarchists' moment has finally come. With the banking system on its knees and capitalism ' floundering, a window of opportunity for real change has arisen. "We need to seize the moment," he says. "There was a moment in May 1968 and another in the 1980s under Thatcher when the miners were on strike, but we failed to grasp either. This one is different. No one's ever seen what we are seeing now with the economy and it's the economy that drives people to the streets."

Bone's own particular brand of anarchism is extreme. "I'm full of class hatred," he tells me cheerfully over a pint in the local Wetherspoons pub after the demonstration. "I just want to overthrow the ruling classes." He was radicalised from an early age: his father was a butler for one Sir Gerald Coke, and the young Bone spent his formative years witnessing him bowing and scraping to his superior. By the age of 15, he was a regular on the Aldermaston CND marches and in 1983 he set up the anarchist journal Class War, "Britain's most unruly tabloid", which still runs to this day.

Although there are no membership figures – anarchists don't deal in such administrative formalities – Bone claims the numbers of people joining the movement has risen significantly in the past six months. But what makes him more convinced that the anarchists' moment has come is that the types of people joining are entirely different.

"Traditionally, anarchism appealed to young, inner- city types," he says. "Now we've got people coming into the anarchist movement we've never seen before. There's older people, whose pensions or savings have been wiped out, as well as people from the suburbs – the aspirational working-class who voted Tory, bought their own council flats and moved up in the world. These are people who were sold all that stuff about the free-market dream and now are being repossessed or made redundant. Capitalism has failed them and they are angry as hell. In the past we've needed to create rage. We don't need to do that now because the rage is already there."

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Despite his own hardline stance, Bone is astute enough to realise that not all of these "anarchists" want actual revolution. Some simply want to voice their anger at the greed and recklessness of the City, others want peaceful protest, and some just want a ruck with the police. But if there is one uniting consensus among them, it's the belief that there is something fundamentally wrong with a capitalist system that has allowed the rich of the world to carry on getting endlessly richer.

Chris Knight, a professor of anthropology at the University of East London, and one of the co-ordinators of G20 Meltdown, describes himself as moderate. "I'm the kind of anarchist that adheres to some form of organisation," he says. "I'm not into throwing bricks through windows; what I'm talking about is something closer to revolutionary, or anarcho, communism."

Since the economic crisis began, Knight has regularly taken to the streets brandishing a placard reading, "Eat the bankers". "We haven't got any secrets," he tells me. "On 1 April, we fully intend to overthrow the Government. ' Gordon Brown is on his last legs, this is his last throw of the dice. The revolution starts here."

Knight adds that 1 April is a date that is highly pertinent to the anarchist calendar: it's exactly 360 years to the day that the Diggers, the English civil-war revolutionaries and arguably the UK's first anarchistic group, set up an independent commune and issued a call for equality.

"If we succeed," Knight continues, "and New Labour falls, we say let's immediately nationalise all banks and redistribute the wealth. In other words, we take the power and we don't let the bankers dictate to us any more. We stop the money pouring into bankers' pockets, where it disappears, and start giving it to the people who will spend it – students, single mums, the unemployed. We need to spend money to stop this country going bankrupt: well, that is a solution.

"It's seismic," Knight concludes. "There has already been a whole balance-of-power shift and the world has been turned upside-down, but it's all happened peacefully. There is going to be a velvet revolution. Not a violent one."

Commander Bob Broadhurst of the Metropolitan Police doesn't seem to think so. He has £7.2m earmarked for the police operation from Wednesday until the conclusion of G20 and believes there to be "unprecedented" planning between protest groups, which are now using technology such as Twitter to organise themselves. What further worries him is that certain groups – Reclaim the Streets and the anarchist group the Wombles, for example – that have lain dormant for much of the boom years of the noughties, are showing signs of remobilisation. Groups such as these are the ones that gave the authorities such an enormous headache throughout the 1990s – from the poll-tax riots in 1990 to the protests over the Criminal Justice Bill in the mid-1990s and finally the violent Reclaim the Streets protests at the end of the decade.

Alexander Callinicos, professor of European Studies at King's College, London, who is speaking at this week's demonstration, backs up Broadhurst's belief that new allegiances between protest groups are being forged. He went to an anti-capitalist demonstration on Halloween last year at Canary Wharf following the collapse of Lehman Brothers. "It was an unusual event," he says, "because for the first time there was an unlikely alliance between anarchists, Marxists and other groups that don't usually get on terribly well. Whatever our disagreements, we are all united in the belief that the blind hunt for profit leads to catastrophe. That is what has brought us all together."

Like his fellow protesters, Callinicos is feeling buoyant about the situation. "I have high hopes for this week," he says. "The economic crisis has exposed the bankruptcy of capitalism and the dire need for an alternative. Anyone who feels there is something fundamentally wrong with capitalism is entitled to feel this is their moment."

But is this all just talk? Is the country really ready for revolution? Tim Harford, Financial Times journalist and author of The Logic of Life (just published in paperback) doesn't think so. "The last time we had a really bad economic depression, we got National Socialism and I'm sure this isn't the alternative these guys have in mind. We have to ask the question, is it really all that bad? Unemployment is clearly terrible but it's nothing like America in the Great Depression of the 1930s. In 1981, it was also bad, it was a rotten time. But was that the end of capitalism as we know it? People have a tendency to engage in wishful thinking. Journalists want it to be really appalling because it makes an exciting story; anarchists want it be the end of capitalism because that's what they've spent their lives hoping for; and economists think that it's nothing really that remarkable."

Nor does Harford think it's time for capitalism to be brought to its knees. "Clearly the free market has its faults, but no one could argue we haven't all done very well out of it in the West," he says. "It's lifted an awful lot of people out of poverty. Generally, the places in the world that have not been successful in letting the market take off tend to be the places that are poorer. Capitalism has had a fairly good track record. I hope it's not on its last legs because I doubt it could be replaced by anything more effective."

Meanwhile, back at the flash-mob gathering, Madonna's "Material Girl" has started up and the obligatory crazy dancing has broken out. Tamsin Omond, one of the five who were arrested after climbing on to the roof of the House of Commons in a protest against the expansion of Heathrow, and the current poster girl for climate change, is right in the thick of it. "What shall we chant?" she asks her friend breathlessly. "Something about banks, maybe?"

"Stupid twat," says Ian Bone. "Listen to her accent. She's just one of those climate-change lot who do a bit of environmental action to get it on their CV before going back to live in their big house with mum and dad. You watch: she'll be an overpaid environmental consultant before you know it."

If this is the unity Commander Broadhurst is so worried about, perhaps he can relax a little. It's hard to tell if anything really has changed; today, it looks like the same old faces doing the same old thing. Should we really be in fear of revolution? We'll have to wait until Wednesday to find out.

Here comes trouble: A brief history of anarchy

1649

The Diggers, a group of agrian communists, are formed. They believe man can be free only in a society without government interference, wherein all products are shared

1780

Anti-Catholic riots are led by Lord George Gordon; 60,000 people proclaiming "No Popery" march on Parliament. Homes are burned, churches attacked and prisoners freed. Nearly 300 are left dead

1840

In "What is Property?", the French political writer Pierre-Joseph Proudhon coins the slogan "Property is theft". He is the first person to define himself as an anarchist

1868

Mikhail Bakunin founds the Social Democratic Alliance with the doctrine of Collectivism and the belief that anarchy is possible only through violent revolution

1876

Prince Peter Kropotkin of Russia renounces his royal title and develops the theory of anarchist communism. He also helps found the London-based Freedom Magazine, still published today

1911

The Siege of Sidney Street between the police and two Latvian burglars. The stand-off ends in death for the Latvians, who have become anarchist heroes for resisting the authorities

1936

During the Spanish Civil War, anarchist militias gain control of much of eastern Spain. Autonomous libertarian villages are set up, money is abolished and the land is tilled collectively

1972

The Angry Brigade, also known as the Stoke Newington Eight, a British libertarian militant group, is responsible for bomb attacks between 1970 and 1972. Strongly influenced by anarchists, their targets include banks, embassies and the homes of Tory MPs.

1976

"Anarchy in the UK", the first single by the Sex Pistols, is released on 26 November. The three-and- a-half minute song reaches number 38 in the UK charts. Its lyrics espouse a nihilistic concept of anarchy

1983

Class War, a cobbled-together tabloid newspaper that has become the voice of the movement, is founded by Ian Bone. The cover, right, refers to the birth of Prince William

1994

The anarchist Zapatista army declares war on the Mexican state and seizes part of their Chiapas homeland, and in the process kickstarts a resurgence in the global anarchy movement

1999

J18, an international day of anti-capitalist protest on 18 June, coincides with the G8 summit. A battle breaks out as 5,000 people converge on the London International Financial Futures Exchange

2008

A young schoolboy is shot dead by police in Athens, resulting in four weeks of rioting across Greece. Anarchists seize control of government buildings. Similar riots kick off in other parts of Europe

Anarchy in the EU: How one boy's death sparked riots across Europe

The demonstrations that took place in cities across Europe last December, as protesters took to the streets in solidarity with Greek rioters, were a stark indication that anarchism is alive and kicking throughout the EU. In Athens, it was the shooting of 15-year-old Alexis Grigoropoulos by police that triggered weeks of violent clashes between the authorities and youths frustrated by government corruption, crony capitalism and high unemployment. Almost immediately, France, Germany, Spain, Italy, Sweden and Denmark saw unrest and, in some cases, similar outbreaks of serious violence, sparking fears that mass insurrection was the shape of things to come.

While many of the protestors were quick to identify themselves with a unified anarchist scene, political commentators agree that in reality, the European picture is ideologically and strategically fragmented, composed of more or less self-contained groups. In each country, individual factions are engaged in their own specific battles with the political establishment, from economic to environmental issues, linked only by a broad anti-capitalist, anti-imperialist stance. Although overlaps with the ultra-Left exist, leading to widespread confusion between the two, what ultimately separates anarchist groups is their belief in practical, militant action.

Not surprisingly, the European countries in which the anarchist movement tends to be strongest are those in which a capitalist status quo exists, as is the case in Germany, Switzerland and Scandinavia. In Greece, Italy and Spain, the situation is aggravated by a deeply felt divide between the Right and Left, and – in the case of the latter two – relatively fresh memories of right-wing dictatorships.

Nevertheless, recent events suggest that anarchist activity is on the rise in nations where it has not previously been a major concern. In France, for example, where a strong far-Left has traditionally stifled any anarchist movement, the Interior Minister Michèle Alliot-Marie has spoken of a serious threat from "ultra-Leftist" and "anarchist" terrorists. In November, nine members of a group of young men and women living in a commune in southern France were arrested in connection with sabotaging the power supply to high-speed train lines and "associating with wrong-doers with terrorist aims". All but one of the "Tarnac Nine" has now been released, amid accusations of absurd heavy-handiness on the part of the authorities.

Rhiannon Harries