They dressed in black, masked their faces and flew red and black flags as if they were a revolutionary army, but anarchists who smashed up shops, banks and hotels during last Saturday's anti-cuts protests in London have dismissed government allegations they are "mindless thugs".

Amid growing public anxiety about the actions of the so-called black bloc, the home secretary, Theresa May, this week threatened pre-emptive police action while Kit Malthouse, London's deputy mayor, branded them "fascist agitators".

But unmasked and talking to the Guardian, anarchists involved in last weekend's violence claimed their direct action tactics were going viral. They said they were legitimate representatives of the public's concern about public sector cuts and their ranks had swollen to an estimated 1,500, boosted by student first-timers.

The black bloc tactic involves masked militants moving in tight units cordoned by flags, vandalising symbolic property and sometimes attacking police. The group created chaos in central London's busiest shopping area last weekend, seizing attention from about half a million peaceful anti-cuts protesters on a Trades Union Congress-organised march and terrifying onlookers. Anarchists attacked the Ritz hotel, smashed the windows of banks, fought with police officers and vandalised police vans. There were 201 arrests (mostly non-violent protesters at Fortnum & Mason) and at least 84 people were injured including 31 police officers, 12 of whom required hospital treatment for minor injuries.

One activist admitted criminal gangs and small numbers of football hooligans were among those who adopted the approach. But the anarchists stressed that those in the black bloc last weekend included graduates, social workers, students, the unemployed, militant feminists and mental health nurses.

The anarchists who agreed to talk also revealed their own deeper motivations: anger at family poverty as they grew up, the exhilarating sense of belonging they found in the black bloc, and longstanding grudges against the police. All of them said the failure of the peaceful anti-Iraq war march to overturn government policy was formative in their decision to turn to aggression and violence over the cuts.

"We realised that political change in this country isn't predicated on being right and winning a debate," said Peter Wright, a twentysomething teacher who was in the black bloc with the South London Solidarity Federation, "which seeks to destroy capitalism and the state".

"You have to force your agenda. The slogan on Saturday was to make the country ungovernable," he said.

On Saturday, some anti-cuts activists plan to occupy Trafalgar Square and have asked anarchists to attend even though the opprobrium they drew after the march has sparked a debate inside the movement about whether their tactics are self-defeating. Nevertheless, with the royal wedding and May Day around the corner police are braced for more unrest.

"We are not in any way setting out to terrorise the public. We are the public," said Robert James, a smartly turned-out unemployed anarchist in his mid-20s. "We should do our utmost to ensure no one is harmed, but we can't guarantee that people will not be shaken up by scenes of disorder … We are not calling for political reform or changes to the tax system. We are sending a clear message to capitalism that we can't be bargained with. There is no reform. We only seek your abolition."

Jason Sands, 32, a graduate and local authority IT worker in south London and black bloc veteran, said the ranks of anarchists appeared to be "growing in confidence, skill and numbers". He said there had been an influx of students galvanised by last year's violence at the Conservative party headquarters in Millbank Tower during anti-tuition fees protests and by police tactics used against conventional demonstrators such as kettling.

"It feels good to be part of it," Sands said. "You are in a group of people who have a shared outlook which you don't always feel in normal life. It can feel exhilarating running down a street and moving as a group. It is an atmosphere of resistance, not of chaos. You could get hurt or arrested so you have a combination of fear and adrenaline and a sense that this is the moment to act because it could all end shortly. There's an intensity to the moment. It is not just about breaking things. It is manifesting your politics and personal feeling in the street."

He said some anarchist protesters only turned up if there was going to be a black bloc, finding it "boring" otherwise. Both Sands and James traced their anarchism to their experience of growing up relatively poor in the 1990s. "I have been going on protests since my parents took me on CND marches and anti-poll tax protests," said Sands. "I realised kids from other families had more stuff and bigger houses but the most acute thing was the poll tax."

After university he found marches in London too "institutionalised" and became involved in violent action abroad, taking part in anti-G8 action in Rostock, Germany, in 2007, during which the offices of Caterpillar, the bulldozer company, were firebombed.

James said he was radicalised when he saw his working-class family fall behind during the consumer and debt boom.

"People growing up in the 1990s experienced capitalism moving away from the production of goods towards finance capitalism and the movement of debt," he said. "Social mobility was everything but was quite difficult to attain. We achieved that through consumption and financed it through debt. Those who weren't able to do that, especially as children, found themselves becoming the collateral damage of the consumer war." He later went on anti-war marches and found himself feeling "utter contempt" for the state.

"You would be incredibly surprised by the demographic that uses black bloc tactics, in terms of age, gender, occupation," James said. "The media like to paint a picture of hooligans and thugs, mindless men on the rampage. It is simply not true. There are women and probably transgender people too. Some of the scariest-looking anarchists work in jobs like social care and mental health. It doesn't come from a thuggish place."

The anarchists named in this article insisted on using pseudonyms.