Celebrities, entrepreneurs and politicians have called on the Government to end the so-called "war on drugs" and urgently review the UK's laws.
In an open letter published in The Times, Virgin Group founder Sir Richard Branson, musician Sting and comedian Russell Brand are among a group of nearly 20 signatories pushing for change.
The letter claims the £3 billion spent on drug policy "does little to address the root causes of addiction and pointlessly criminalises people".
The initiative, led by Green MP Caroline Lucas, has attracted cross-party backing from Labour MP Keith Vaz, Conservative MP Zac Goldsmith and Liberal Democrat MP Julian Huppert.
The letter comes as politicians debate a Home Affairs Select Committee report that warns that Government action is needed "now, more than ever" to consider all the alternatives for drug policy.
It reads: "Worldwide there is growing recognition that the 'war on drugs' has failed - having cost billions of dollars and caused tens of thousands of deaths.
"In the UK, scientists, politicians, lawyers and police increasingly agree that we need to review existing policy, which costs taxpayers £3 billion a year but does little to address the root causes of addiction and pointlessly criminalises people.
"By agreeing to an independent review to determine whether the Misuse of Drugs Act 1971 is effective or good value for money, the Government can prove its willingness to acknowledge failures within existing policy - and join in the global effort towards an alternative strategy based on evidence."
The Home Office is undertaking a detailed study of how other countries deal with illegal drugs including forms of decriminalisation. Ministers are being sent to countries such as Portugal, which has ''depenalised'' small-scale possession, to gather evidence on what works.
But calls in the Home Affairs Select Committee report for a wide-ranging royal commission earlier this year were rejected by the Government, which insisted there was no case for "fundamentally rethinking the UK's approach".