Sir Richard Branson and Dame Judi Dench have called for the Government to consider decriminalising drugs as its current policy was condemned as a failure.
The Global Commission on Drug Policy, whose members include former United Nations secretary general Kofi Annan, warned that major policy reforms were needed to help reduce the prison population and stop wasting millions of pounds.
Dame Judi backed calls for the "immediate decriminalisation of drug possession" should a policy review show it has failed while Sir Richard said a new approach was needed.
"One that takes the power out of the hands of organised crime and treats people with addiction problems like patients, not criminals," he said.
Dame Judi urged David Cameron to carry out "a swift and transparent review of the effectiveness of current drug policies".
The Oscar-winning actress was one of more than 30 high-profile figures, including Sir Richard, who signed an open letter to the Prime Minister, saying: "Should such a review of the evidence demonstrate the failure of the current position we would call for the immediate decriminalisation of drug possession."
Nearly 80,000 people in the UK were convicted or cautioned for possessing an illegal drug in the last year alone and "most were young, black or poor", the letter published by campaign group Release said.
The intervention of high-profile public figures, backed by many others including Sting, actor Julie Christie and former defence minister Bob Ainsworth, comes as a report by the Global Commission on Drug Policy said action was needed "urgently" and "policies need to change now".
"There are signs of inertia in the drug policy debate in some parts of the world as policymakers understand that current policies and strategies are failing but do not know what to do instead," the report said.
The commission called for UN Secretary General Ban Ki-moon to help create "a truly co-ordinated and coherent global drug strategy that balances the need to stifle drug supply and fight organised crime with the need to provide health services, social care, and economic development to affected individuals and communities".
