The war on drugs is working really well, isn't it?
Legalise absolutely everything, and sell it in state-run premises for the cost of production or, indeed, at a flat-rate quid a go. You might even experiment with giving it away.
People who take it will get clean, safe, properly made drugs which are far less harmful than street adulterated drugs. They will have access to a range of cessation services. They will not be pressurised to move onto more harmful substances by dealers with a commercial interest in addiction. The dealers will be put out of business.
It's not a panacea, for the same reasons as improved car security have made car crime different, and the Good Friday agreement didn't cause paramilitaries to all get jobs as accountants. But a large level of acquisitive crime will simply evaporate, as drug users will no longer need to use crime to fund their drug use.
The crimes that the more serious criminals (those that, to quote Biggie Smalls,not "Never get high on your own supply") commit won't be reduced in the same way because they will move onto other crimes. But those crimes won't have the same ambiguous social support, so will not enjoy the same de facto acceptability: there are a lot of people who are otherwise law-abiding invested in being able to buy drugs, but who are not similarly invested in supporting their local protection racket.
The collateral damage will be people who willingly take the newly legal drugs may get fucked up by them, although as the drugs will be of known quality and dosage far fewer as a proportion of users than currently. The question is whether fucked up users of legal drugs is more, or fewer, fucked up people than fucked up users of illegal drugs plus the casualties of the drugs war.
But it does seem that "eradicating drug-fuelled violence from London" isn't likely, so trying something else might be worth a go.