In a confidential briefing for the Prime Minister, the report says that tackling dealers would not necessarily stop the crime wave caused by addicts.
The report, which the Government released on Friday night under cover of the Live8 concerts, is one of a series of top-secret policy documents forced into the open by the Freedom of Information Act.
The briefings contain embarrassing information about how some government policies are failing - on the war against drugs, health, transport, crime and education. They were all either written or overseen by Lord Birt, the former director general of the BBC and friend of Mr Blair.
The report on health concludes that "versus comparator countries, Britain is short of medical capacity along almost every dimension". It suggests sending more patients abroad for treatment.
The drugs report, large parts of which have been withheld under exemptions in the Freedom of Information Act, reveals that "those engaging with treatment tend not to stay with it for long".
It adds that tackling drug dealers is a problem because "the drugs supply business is large, highly flexible and very adaptable; over time the industry has seen consumption grow and prices reduce".
The Government decided to withhold further embarrassing parts of the report under the Freedom of Information laws but it has been leaked.
The unpublished extract says that the international drugs war is driving cartels to move their operations elsewhere. It says: "Effective efforts at eradication of coca growing in Colombia are thought to have displaced crops to Peru and Bolivia."
The report says about efforts in the war against drugs in the UK: "Interventions at every stage of the production, trafficking, wholesaling and dealing process have resulted overall in modest seizure rates of up to 25 per cent of total production." It adds: "Even if supply-side interventions were more effective, it is not clear that the impact on the harms caused by serious drug users would be reduced."
The report has been seized on by those who want a rethink of the criminalisation of drug use in Britain. The drugs policy think-tank Transform said that Lord Birt's report strengthened the case for reform of the drugs laws.
"This report is a thorough indictment of a policy that enjoys broad international and domestic support but cannot withstand basic scrutiny. It demonstrates what drug law reformers have been saying for decades, that the war on drugs has failed and is often actively counter-productive," said Danny Kushlick, the director of Transform.
The report says that 280,000 users of heroin and crack are responsible for 87 per cent of the cost of drug-motivated crime in the UK.
It concluded that only 20 per cent of users that commit crimes to fuel their habit "are receiving treatment ... Those engaging with treatment tend not to stay with it for long".
There are 30,000 addicts who commit more than half the drug-motivated crime in Britain. An analysis of the effect of certain drugs on crime and health found that while crack and heroin are incredibly dangerous, both to the health of the user and to society, cannabis and cocaine areless harmful. It says use of cocaine, cannabis, ecstasy and LSD is "unlikely to motivate crime".
Drug addicts who commit crimes to feed their habit take heroin or crack, or a combination of the two and are most likely to be found in "deprived urban areas". The highest concentrations of criminal drug addicts are in Liverpool and the East End of London. The lowest concentrations are in Surrey.