Ben Rogers, now a visiting fellow at the Royal Society for the encouragement of Arts, said that people should learn how to restrain offenders as well as self-defence and defusing tense situations.
He said that although there were concerns about the vigilante gangs from particular ethnic groups that formed during last summer's riots, they showed "civic pride" and a desire to uphold the law.
And Mr Rogers added that cuts of up to 20 per cent in police budgets, together with the outsourcing of many forces' functions, will prevent frontline officers from being able to deal with all low-level disorder by themselves.
His comments come after ministers said that householders and shopkeepers should be able to use "reasonable force" to tackle burglars.
Mr Rogers said: "With the real prospect of traditional police patrolling being scaled back, now is surely the time to focus seriously on agreeing the core skills that active citizens need - individually or collectively - if they're to step up to the mark.
"The Coalition Government has signalled its determination to encourage and support citizens to 'have a go' and intervene to stop criminal behaviour. But to do this - citizens need training - and the Government needs a strategy if these emerging ideas are to be supported and developed."
In a new RSA report, published on Wednesday, Mr Rogers said that anti-social behaviour - including people being drunk and disorderly, violent, carrying out littering or vandalism - is a "stubborn problem" that leads to fear of crime as well as undermining confidence in law and order.
But while there is a limit to what police can do to tackle it, Britain is increasingly a "walk on by" society where people are unwilling to take a stand.
This situation is set to worsen as police budgets are cut, despite politicians' desire to encourage "active citizenship" and the "Big Society".
Mr Rogers suggested that the model used to spread first aid could be adopted for the public safety message, with experts teaching simple skills.
He said some charities and public bodies have already started courses along these lines, with park-keepers and housing estate managers taking part as well as pub landlords and shopkeepers.
They are being taught how to "read a situation" and decide whether or not to intervene, as well as how to ward of an attack and "restrain an assailant" and perform a citizen's arrest.
Other lessons on "defusing and mediating" teach people how to talk to people who are upset and calm down quarrels.
As well as training from police professionals, which could be expensive and time-consuming, Mr Rogers said such skills could be taught by "lay trainers" in the same way as experienced mothers teach childbirth techniques. Courses could also take place online.
"If ordinary police officers were significantly and systematically involved in offering training to the public in how to address anti-social behaviour and deal with aggression and conflict, this might have a significant impact on how citizens see their role in supporting good public safety outcomes," he wrote.
An afterword to his study suggested that the new Police and Crime Commissioners, who will be elected in 41 areas across England and Wales in November, could draw up law and order strategies that "draw on citizens' capabilities" as force budgets are squeezed.