The liberal attitude of Danish authorities to drugs is being tested this weekend, with addicts taking to the streets of Copenhagen to sell a new Big Issue-style magazine with the explicit aim of funding their addictions.

Five thousand copies of the magazine, with a cover price of 30 krone (£3.40), are being sold on street corners by drug users. Each addict will keep 20 krone to fund drug buying, according to the publishers of the magazine, which is to be sold under the title Illegal. If successful, the publishers say they plan to bring the magazine to the streets of London.

Michael Lodberg Olsen, a self-styled social entrepreneur who is using his own money to finance the magazine, said the idea was to give addicts some dignity and an alternative source of income to prostitution and crime.

Olsen, who is known in Copenhagen for his work trying to help addicts rebuild their lives, said that eight would be selling the magazine this weekend, but that he expected many more to join up in coming days.

"As a civil society we cannot decide to decriminalise drug users," Olsen said. "But we can make them a little less criminal, bring a war, which has failed, into focus, and create more dignity for them.

"The question is not how much cocaine you can buy for 20 krone. The question is why we, as a society, accept that the police and drug users are on the same treadmill after so many years.Couldn't we use the resources better? Couldn't we start seeing these things in a new way?"

The first few copies of the magazine were sold on Friday, with the first addict to begin selling the issue finding buyers for £18 of magazines in just a few hours. Olsen said that he expected there to be enough demand for four editions of the magazine a year.

However, the conservative Danish People's party has already said it is against the publication, claiming that it would only encourage drug abuse, which – while relatively limited across the country – is concentrated in Copenhagen and the former meat-packing district of Vesterbro.

Olsen, whose previous ventures have included a mobile drug-injection room to allow users to feed their habit in a safe and discreet environment, said he was not troubled by the controversy.

"Some people won't like it, they will say these people should get treatment," he said. "I say, what planet are you living on? No one has solved the problem of drug addiction, so is it not better that people find the money to buy their drugs this way than through crime and prostitution?

"We hope to sell 10,000 copies of each edition in the future, and then we will come to London."

Olsen's mobile drug-injection room – a van in which addicts are able to inject under the supervision of a nurse – encouraged authorities in Copenhagen to make it the latest city to establish an official drug consumption room for addicts. The room, in Vesterbro, has been such a success in moving drug users off the streets that it is now expanding.

Olsen's 56-page magazine is produced by volunteers and its first edition contains articles on the US war on drugs, portraits from a drug injection room in Aarhus, the country's second-largest city, and a list of the 20 most dangerous drugs, in which alcohol claims the top spot.

Copenhagen has been pioneering a more tolerant attitude towards addicts. Earlier this year, city officials said they wanted to legalise the sale of cannabis for a trial period to better control the sale and consumption of the drug.

Under the plan, cannabis would be sold either from an existing chain of shops or from a local council shop and would be controlled. However, the city's initiative has been blocked by the national government.