An investigation by the RSA says illicit substances can be "harmless", while drinking and smoking can cause as many problems.
It says the law has been "driven by moral panic", and suggests policy-making should be left to drug teams and local authorities.
The Home Office says it does not accept all of the report's recommendations.
Level of crime
Anthony King, professor of government at Essex University, who chaired the Commission on Illegal Drugs, said the "great majority" of drug users did not harm themselves or others.
"Current policy is broke and needs to be fixed," he added.
The RSA's panel recommends scrapping the Misuse of Drugs Act and replacing it with a broader Misuse of Substances Act, and replacing the existing ABC classification system with an "index of harms".
Panel members included Deputy Assistant Commissioner John Yates of the Metropolitan Police.
|| A majority of people who use
drugs are able to use them without harming themselves or others
This would extend the definition of drugs to include alcohol and tobacco - as well as illegal substances, which the report says have been "demonised".
The report, entitled Illegal Drugs, Communities and Public Policy, also calls for so-called "shooting galleries" to be introduced where users can inject drugs as well as wider access to prescription heroin.
It says policy should be about reducing harm and pursuing the criminal gangs behind the drugs trade rather than the level of crime.
If drug taking does not harm anyone, then criminal sanctions should not be applied, the report continues.
The report says: "The evidence suggests that a majority of people who use drugs are able to use them without harming themselves or others.
"The harmless use of illegal drugs is thus possible, indeed common."
It says drugs education is "inconsistent, irrelevant, disorganised", and its main focus should shift from secondary to primary schools.
The Home Office has estimated that the social cost of drug abuse alone to Britain is between £10bn and £17bn a year.
'MOST HARMFUL' SUBSTANCES
4. Street methadone
5. AlcoholSource: Science select committee
It said its strategy has led to a 16% fall in drugs crime and more people able to access treatment.
Martin Barnes from the charity Drugscope said drug use needed to be addressed as a wider social problem.
He added: "There's really far too great an emphasis on it being a problem solely associated with crime.
"It's about public health, it's about poor mental health, it's about homelessness."
Former Conservative leader Iain Duncan Smith said the report was "worryingly complacent".
He added: "The RSA has also failed to do its homework by not surveying the views of drug addicts - who want recovery and drug-free lives - not managed dependency on methadone."
Former home secretary David Blunkett told BBC Radio 4's Today programme he wanted to see "a much more sensible debate" and that he supported a "substantial" expansion of the prescribing of heroin.
But James Griffith-Edwards, emeritus professor of addiction behaviour at the University of London, told BBC Radio Five Live that he was sceptical about the report.
The RSA is a think tank which was founded in 1754
Its Commission on Illegal Drugs was set up in January 2005
It asked: "If current policy and practice on illegal drugs are not working, why not?"
Panel members included drugs experts, academics, politicians and community workers
He said: "I doubt whether any swingeing remedies would get one very far."
However, Liberal Democrat home affairs spokesman Nick Clegg called the report "an extremely important contribution" to the debate, adding: "The so-called war on drugs is failing."
And Steve Rolles of drug law reform campaign group Transform praised the Commission's findings.
"This really is a rational response to 30 years of dramatic failure," he said.
MOST HARMFUL DRUGSGLOSSARY
Benzodiazepines: Wide-ranging class of prescription tranquilisers
Buprenorphine: Opioid drug used in treatment of opiate addiction
4-MTA : Amphetamine derivative sold as 'flatliners' and ecstasy
Methylphenidate: Amphetamine-like drug used to treat ADHD
Alkyl nitrites: Stimulant often called amyl nitrites or 'poppers'