More than 90 celebrities, politicians, lawyers and health experts have written a letter to the prime minister calling for a review of the government's policy on illegal drugs.
The group includes musician Sting, Sir Richard Branson and author Will Self.
They want a change in the law so drug possession is no longer a crime.
The call comes as part of a global day of action against the so-called "war on drugs" and protests are planned to take place in 100 cities on Thursday.
The signatories of the letter to David Cameron also include groups involved in law enforcement, such as the Prison Governors Association and the National Black Police Association.
'Drug policy reform'
Comedian Russell Brand and the barrister Michael Mansfield QC are among those who have signed the letter, which was drafted by the drug charity, Release.
Protests were planned in several cities including Paris, Warsaw, Mexico City and Rome.
In London there was a public gathering on Thursday morning in Parliament Square.
"The global day of action is a public show of force for drug policy reform", said Ann Fordham, who is executive director of the International Drug Policy Consortium, which focuses on issues related to drug production, trafficking and use.
"The tide is turning and governments need to urgently fix their drug policies and repair the damage that has been done," she said.
The letter says the use of legal sanctions for the possession of drugs in the UK has led to the "unnecessary criminalisation" of more than 1.5 million people in the last 15 years.
The letter goes on to state that evidence from Australia, the Czech Republic and Portugal shows that health problems linked to drugs are "dramatically" reduced when users are given medical support and advice rather than being prosecuted.