The multibillion-pound global anti-drug strategy has been left floundering by the rapidly growing industry in so-called legal highs, the United Nations has said.

The number of products – designed to mimic the effects of illegal drugs while remaining on the right side of the law – has surged by more than 50 per cent worldwide in three years, as chemists tinker with ingredients to create new substances.

The report by the UN Office on Drugs and Crime found that Britain was the largest market for new psychoactive substances in the EU with 670,000 people aged 15 to 24 experimenting with them. Mephedrone – a legal high banned here in 2010 – now ranks as the fourth most abused substance after cannabis, cocaine and ecstasy.

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Authorities say that the substances are marketed to sound like low-risk party drugs, with names like Banshee Dust and Purple Bombs, but have not been fully tested and could be more dangerous than traditional drugs.

The UN described them as a “hydra-headed” problem: no sooner is one substance banned than another takes its place, making it difficult to study the long-term impacts on health.

The drugs are openly marketed online and sold legally at hundreds of “head shops”, with substances changing every month to counter bans and to keep up with fashions. “When something’s due to be banned we just stop trading in it,” said one online seller who declined to be named. “We get rid of stock before a ban comes in: to have anything after that is asking for trouble. We keep very low stock for that reason and buy in very small batches.”

Earlier this month, the Government announced a year-long ban on two legal highs known as NBOMe, which has a similar effect to LSD, and the stimulant Benzo Fury. But the nature of the fast-moving industry means that websites, even those named after the now-banned drugs, have re-written their product lists in a legal cat-and-mouse game with the authorities.

Professor Les Iversen, chairman of the Advisory Council on the Misuse of Drugs, has said that more than 200 such drugs were being sold outside of the regulatory framework.

“While new harmful substances have been emerging with unfailing regularity on the drug scene, the international drug control system is floundering, for the first time, under the speed and creativity of the phenomenon known as new psychoactive substances,” said the report by the UN. It said that the number of such drugs increased from 166 at the end of 2009 to 251 by mid-2012.

The industry said that it was being unfairly harassed by police and trading standards. “People just like drugs,” said one entrepreneur with a small-scale operation in legal highs. “There’s a stigma but people do it. The problem with junkies is that they give drug users a bad name.”

Jeremy Browne, the minister responsible for crime prevention, said: “The UK is leading the global effort to address the serious threat from ‘legal highs’, adapting and innovating as new trends emerge.”

Professor David Nutt, chairman of the Independent Scientific Committee on Drugs and former government adviser, said the findings should make the government abandon its argument that illegal drug use was falling.

Prof Nutt, who was sacked after clashing with the last Labour government over drugs classification, said: “Not even the lawyers and drug chemists know what’s legal or illegal anymore.”

He said a ban might stifle the spread of “a nasty new drug” but speeds up “the creation and sale of new things even nastier and less familiar”.

“Falling use of illegal drugs (mainly cannabis) is no victory if they are replaced by a succession of untested drugs from Chinese labs,” he said.