The arrest of leaders of criminal gangs in the wake of last year's riots has led to an increase in "chaos, violence and anarchy" in neighbourhoods across the country, a report has claimed.

Prime Minister David Cameron promised an "all-out war on gangs and gang culture" following the riots which brought mayhem to many English cities in the summer of 2011, and police have responded by arresting many of those associated with criminal groups.

But the report by the Centre for Social Justice (CSJ), obtained by The Observer ahead of its publication on Monday, found the removal of established gang leaders has led to the breakdown of criminal codes of behaviour and a "marked increase" in violence.

The report said: "Many in Whitehall regard the riots as a random one-off, and mistake the quashing of the disorder as control of the streets. They could not be more wrong.

"The alarming fact is that many streets across the country are besieged by anarchy and violence. There is no control in such neighbourhoods."

The report said that people it spoke to in riot-hit areas reported a "marked increase" in the violent behaviour of some gangs as the result of the removal from the streets of "elders" who had previously imposed a code of behaviour. "There was a consensus that the current gangs neither have such a code nor cohesive leadership, which is resulting in increased chaos, violence and anarchy," it warned.

Christian Guy, managing director of the CSJ, which was founded by Work and Pensions Secretary Iain Duncan Smith, said: "Gangs played a significant role in the riots and it is dangerous to pretend otherwise. In London at least one in five of those convicted was part of a gang."

The CSJ report recommended "addressing the drivers of gang culture, not just the symptoms". It said: "The surest way of eliminating gangs is to try to ensure that children and young people never want or feel the need to join them. To do this we need to tackle deeper issues in our society and seek to nurture and support ever-strong families and stronger communities."

A Government spokesman said: "Our Ending Gang and Youth Violence strategy makes clear this problem cannot be tackled through police enforcement alone. That's why a £10 million fund is helping to stop the next generation of gang members as well as targeting those already involved in violence.

"There's also a new network of Young People's Advocates to provide direct support to victims of gang-related sexual violence and we introduced gang injunctions for 14-17 year olds. There are no quick fixes but we are seeing results. The Crime Survey for England and Wales shows that crime is down by 6%, and police figures show knife crime is down by 9%."