Britain may face years of public disorder fuelled by the economic crisis, with police battling to keep control of the streets, a former Scotland Yard chief has warned.

Lord Stevens made his warning at the launch of an independent commission into the future of policing, which has been set up by Labour as it tries to outflank the government on law and order.

A senior police source told the Guardian that Stevens's warning was shared by most police chiefs and Scotland Yard said: "We anticipate the potential for the increased demands of both peaceful protest and greater criminal disorder threats from a minority continuing into 2012. Our resourcing levels and tactics will reflect lessons learned from 2011."

Stevens said the way that outbreaks of public disorder are policed will be a key issue, given police failings when England was hit this summer by some of the worst riots in living memory: "The next 18 months, two to three years, one of the main issues will be public order, or rather public disorder." Asked what could be causes of the disorder, Stevens said: " Looking ahead into the crystal ball, I think you can see there is disquiet on the streets. I'm really concerned about youth unemployment, and unemployment generally, I'm really concerned about signs of increasing crime. My gut feeling and beyond, is that it's going to be a very difficult 18 months [to] two years. I hope that I'm wrong, but I don't think I am."

He said he hoped any disorder would not be on the scale of the summer riots of 2011 but warned that "the police will have to be match-fit on this issue".

Stevens said the police response to this summer's riots led them to lose control of the streets. He added that the first riot in Tottenham, north London, after a police shooting, should have been anticipated. During the summer riots police had been "acting a day behind"' events, he added.

Stevens said it "rang alarm bells" that stop and search was an issue, and police must be better at explaining to communities what they are doing and be better at listening to their concerns.

Some of the concerns raised by Stevens echoed the findings of the Guardian/LSE's Reading the Riots study, which has revealed that a key factor in the August riots was discontent with the police, with stop and search one of the most hated aspects. A Whitehall source said ministers rejected Stevens's analysis, saying there was nothing to indicate there would be renewed disorder; nor was it inevitable rising unemployment would lead to trouble. The source added the government view was the cause of the summer riots was "not about deprivation or distrust of the police, it's about getting free stuff". Tough sentences would act as a deterrent and the police were now better able to quell trouble. But Stevens's warnings carry weight not just because of his tenure as Britain's top officer, but because he has been courted by and advised both Labour and the Conservatives.

The government's draft strategic policing requirement, published last month, says: "Police forces need to ensure they can keep the peace by managing public disorder and both facilitate peaceful protest and protect the rights and safety of wider communities when responding to large scale public protests."

The inquiry that Stevens will chair, which will report by 2013, is the first in five decades to promise a root-and-branch examination. It comes as police face large cuts, with rank-and-file officers saying cuts to their pay and conditions have hit morale. The government says it can protect frontline policing and that police forces, which grew under Labour, can cut crime for less money. Labour says the coalition government rebuffed its calls for a royal commission into policing, so it effectively set up its own. Stevens, the last commissioner of the Metropolitan police to complete his term in office, warned the government not to be "insulting" or "arrogant" in dismissing the work of the panel of academics and former police chiefs that he will chair.

Paul McKeever, chair of the Police Federation, said: "We welcome the independent commission – it's going some way to what we've been calling for for years, to look at things in a holistic way, rather than in a piecemeal way, as the government has done." The policing minister, Nick Herbert, has said it was wrong for Labour to be "subcontracting decisions on police reform – reform which they espoused in government and are now opportunistically opposing – to a committee". The shadow home secretary, Yvette Cooper, said: "My fear is that policing in Britain now faces a perfect storm. The scale of the cuts, the chaos of confused reforms, escalating demands and declining morale."

She added: "I am now worried about the future for policing and the risk of a growing gap between public concerns and the capacity of the police to deliver."