MPs have backed a move to downgrade cannabis, putting it in the same group as tranquilisers and steroids.
Cannabis users will generally no longer be arrested for possession
The reclassification of the drug from Class B to Class C was supported by a majority of 156, despite Tory warnings it would lead more young people into harder drug use.
Junior Home Office minister Caroline Flint rejected claims that cannabis would become "semi-legal", claiming the move was part of an "honest and credible" strategy to tackle the wider drug problem.
The changes, which will come into effect in January next year, mean penalties for possession of the drug will be lessened, but dealers could face up to 14 years in jail.
Under guidelines drawn up by the Association of Chief Police Officers last month, police will also retain the power to arrest users in special circumstances, such as when the drug is smoked outside schools.
The Conservatives have described the move as "liberalisation", with shadow home secretary Oliver Letwin declaring the government's drug policy a "dreadful muddle".
And the Police Federation, which represents 130,000 police officers, is also against downgrading the drug to Class C.
Chairman John Barry said the reclassification sent out "a confusing and conflicting message", especially to young people.
Mr Blunkett believes the law must be changed to let police spend more time dealing with more harmful Class A drugs like crack cocaine and heroin which account for more crime.
At the moment, about 80,000 people are arrested and fined for cannabis possession every year.
After a change in rules, anyone caught in possession of cannabis will only receive a warning and will have the drug confiscated.
But some drugs law campaigners are concerned about a failure in the guidelines to spell out the amount of cannabis deemed as being "for personal use".
Danny Kushlick, director of Transform, a national charity campaigning for reform, said that while the health impacts of cannabis were hotly disputed, it was obvious that illegal production was less safe than if it were regulated.
"The only way to ensure that cannabis users are aware of the strength, purity and potential dangers of cannabis is to legalise, regulate and control its production and supply," he added.
But Lesley King-Lewis, chief executive of Action on Addiction, said the move would increase cannabis use.
She said: "As many as one in 10 cannabis users become addicted. Cannabis use is associated with cancers of the mouth, tongue, throat, oesophagus and lung and reductions in fertility as well as with mental illnesses such as schizophrenia and depression."