The budget increase - enough to build about four new hospitals - is the largest amount ever set aside to deal with the drug problem, said a Government source.
Dr Cunningham, who has taken over responsibility for the Government's anti-drugs strategy, will this week set out the change of direction.
"Last year, two-thirds of the money spent on drug misuse was spent on those who already have been sucked into drugs and crime. The new strategy will change the emphasis so that spending on stopping the problem from happening will rise by 25 per cent by 2002," said a Government source.
The majority of the extra funding, earmarked for the anti-drugs campaign by the Chancellor in the Comprehensive Spending Review, will be spent in improving the Prison Service strategy to help to reduce re-offending.
Under the new arrangements, there will be pilot schemes to ensure follow- up drug treatment, and the forthcoming Crime and Disorder Act will urge courts to force offenders to take treatment within the terms of community service orders, instead of sending them to prison where they are likely to be exposed to more illegal drugs.
"These measures get tough on drug-related offenders by getting them into treatment and ensuring they stay there," said the source. "They will be rigorously enforced on people who have committed crimes such as shoplifting and burglary to fund their drug habit."
Dr Cunningham will warn that drugs destroy lives and ravage communities. "They are an active breeding ground for crime and can pull families and communities apart. Enough is enough," he will say. The money will be directed at health treatment, rehabilitation and education.
Government research has shown that more than half of young people under 25 use illegal drugs and that almost half of all recorded crime is drugs related in some way. There are estimates of 100,000 to 200,000 drug addicts in the UK.
Ministers have rejected calls for legalisation of cannabis as a way of tackling drug-related crime. The new measures will reinforce the Government's message that prohibition of drugs, coupled with tough policing, is still seen as the best way to combat the problem.