Dame Judi Dench, Sting and Julie Christie have urged David Cameron to decriminalise possession of all drugs.
In an open letter to the Prime Minister, they called for "a swift and transparent review of the effectiveness of current drug policies".
"Should such a review of the evidence demonstrate the failure of the current position we would call for the immediate decriminalisation of drug possession," they wrote.
Sting added: "Giving young people criminal records for minor drug possession serves little purpose - it is time to think of more imaginative ways of addressing drug use in our society."
The letter, which is also signed by former defence secretary Bob Ainsworth, actor Kathy Burke and three former police chiefs among others, comes as the Global Commission on Drug Policy, whose members include entrepreneur Sir Richard Branson, said the war on drugs has failed.
They also called for an urgent review of drug policy, with Sir Richard saying a new approach "that takes the power out of the hands of organised crime" was needed.
Regulation and decriminalisation have been shown to work, he said.
The letter, which was published by the campaign group Release, said: "The failure of the current UK system of criminalisation is clear.
"It is time for the UK to review its policy and adopt a health-focused, evidence-based approach to drug use."