Dame Judi Dench, Sir Richard Branson, and Sting have joined an ex-drugs minister and three former chief constables in calling for the decriminalisation of the possession of all drugs.

The high-profile celebrities together with leading lawyers, academics, artists and politicians have signed an open letter to David Cameron to mark this week's 40th anniversary of the 1971 Misuse of Drugs Act. The letter, published in a full-page advertisement in Thursday's Guardian, calls for a "swift and transparent" review of the effectiveness of current drugs policies.

Its signatories say that all the past 40 years has produced is a rapid growth in illicit drug use in Britain, and significant harm caused by the application of the criminal law to the personal use and possession of all drugs.