Musician Sting, business tycoon Sir Richard Branson and comedian Russell Brand are among leading figures calling for the possession of drugs to be decriminalised.
In an open letter to David Cameron, more than 80 campaigners urged the Prime Minister to launch a review of Britain's drugs policy.
Leading QC Michael Mansfield, the National Black Police Association and the Prison Governors Association are also among the signatories highlighting how more than 1.5 million people have been criminalised in the UK for drugs possession over the last 15 years.
The letter points to research which shows that drug laws are disproportionately used against black people in England and Wales - they are six times more likely than white people to be stopped and searched.
Nick Glynn, vice president of the National Black Police Association, said: "It is time for a mature, informed, objective debate around the UK's drugs laws.
"Enforcement of the 1971 Misuse of Drugs Act has created many unintended, negative consequences and new approaches must be considered, including those which have been successful in other countries. Strategies that avoid criminalising people and focus instead on health and education seem to me to offer a positive way forward."
The group also wants a commitment from Government that it will push for an international review on drugs through the United Nations.
It warns that countries such as Colombia, Mexico and Guatemala, where the drug trade has led to hundreds of thousands of deaths, will struggle to tackle the problem without proper support from governments in the West.
Niamh Eastwood, executive director of Release, the organisation leading the action, said: "The drug policy reform debate has moved forward in recent years and the UK Government needs to be at the forefront of it.
"In 2002, when the Prime Minister was a member of the Home Affairs Select Committee, he supported the recommendation that the UN consider alternatives to the status quo. We are asking him to stand by that commitment and recognise the damage that has been done, both nationally and internationally, by repressive drug policies."