The Hotel Lutetia is a beautiful belle époque building in Paris's sixth arrondissement. It's a place steeped in history: Josephine Baker was a resident, and it was here that General de Gaulle spent his wedding night. It was also here, on 26 January 2000, that Dr Olivier Ameisen, first official physician to the prime minister of France under Raymond Barre, noted cardiologist at Cornell University, talented pianist and friend of both Nobel Peace Prize-winner Elie Wiesel and record producer Arif Mardin, received the Légion d'Honneur for his "contribution to the image of France abroad and to cardiology".

A proud moment in a life of excellence and achievement, you would imagine, but you'd be wrong. Sitting in the bar of the Lutetia 10 years later, Ameisen, now 56, recalls how he felt: "When Barre and all those guys were kissing my cheeks, I thought: 'Where are their brains?' I mean, when I was accepted at Cornell I looked at those guys and I thought that they were mediocre – that if those guys want me, they are idiots."

The truth was that Ameisen, for all his successes in life, was consumed with self-loathing and shame. He was a hopeless alcoholic – hopeless in the sense that, though he seemed able to achieve anything else he put his mind to, he could not stop drinking. Despite running a thriving private practice in New York, in his late thirties he had become a binge drinker and by 1997 was regularly being admitted to hospital. He tried any treatment available: tranquillisers including Valium and Xanax, antidepressants and specific alcohol medications including Antabuse and Acamprosate. He underwent acupuncture and hypnosis, took regular exercise and practised yoga. He attended cognitive behavioural therapy and up to three meetings of Alcoholics Anonymous a day. But his drinking only got worse: "The more I drank to ease my anxiety, stave off panic and counter draining insomnia, the more I had to drink for the same effect." No longer trusting himself to treat his patients responsibly, he stopped working altogether. Finally his doctors told him he had "at best" five years of life left.

It's a dramatic but not unusual story. According to the World Health Organisation, approximately two million people around the world die from the effects of alcohol each year, more than from any single form of cancer. In the UK, government figures estimate that one in 13 people is dependent on alcohol. For all the efforts of doctors, therapists, social workers and support groups, only a fraction of those addicted to alcohol manage to stop drinking and remain abstinent for a significant period.

It's not extraordinary that, despite all his efforts and his obvious intelligence and commitment, Dr Ameisen failed to overcome his addiction. What is extraordinary is that he eventually discovered a drug he claims has cured him of alcoholism and that he claims can cure all addictions, including cocaine, heroin, smoking, bulimia and anorexia, compulsive shopping and gambling. Because that is, according to all other schools of thought, simply impossible.

The Ameisen sitting beside me in the bar of the Hotel Lutetia is as far from the popular conception of the alcoholic as it's possible to get. Dressed in a dark blue suit and tie, tanned, relaxed and distinguished, he is very much the successful doctor, rather than the ruined drunk who was in and out of rehabilitation units and even a psychiatric ward. As a recovering alcoholic myself, I no longer expect all addicts to be tramps, but he is certainly a good advert for his method.

The secret of his sobriety, as outlined in his book The End of My Addiction, first published in 2008 and reissued in the UK this month, is a drug called baclofen. Formulated in the 1920s, baclofen is a muscle-relaxant more often used to treat spasticity and multiple sclerosis. It came to Ameisen's attention via a story in the New York Times about a paraplegic addict who found his desire for cocaine decreased when taking baclofen for muscle spasms.

Ameisen already suspected that – contrary to Alcoholics Anonymous's belief in a physical condition with a spiritual solution, and the opinion of most therapists and even psychiatrists – the cause of his addiction might be chemical. In fact he pinned his hopes on it. "In the end," he tells me, "I thought: 'I want to commit suicide.' But I did not because I was convinced that the day I died, the next day they would find a cure. As you're being buried, people will think: 'You idiot – you died too early.'"

In his search for a cure, one particular aspect of baclofen caught his attention: that it was a muscle relaxant. He had suffered from anxiety and muscular tension all his life and was convinced it was at the root of his problem: "I knew that nothing – yoga, meditation, I'd tried it all – could relax my muscles. I was tense from morning to evening." He thought that perhaps it was the same for all alcoholics or even all addicts: "Unconsciously, as a physician maybe, I was observing people at the AA meetings and I saw the foot-tapping and the fingers going – the compulsiveness."

Internet research seemed to confirm his hunch: in one study, baclofen was shown to have an effect on panic attacks; in another, "obsessional thinking about alcohol disappeared"; in a third, it suppressed the intake of cocaine in addicted rats. All indications were that it was safe, even in high doses. Eventually, in March 2002, he took the plunge and wrote himself a prescription, starting low and gradually increasing his dose.

Almost at once, the effects were positive: "It controlled my anxiety better than any of the standard anti-anxiety medications. It reduced my craving for alcohol and enabled me to remain abstinent for longer periods." He even found he had lost the urge to shop compulsively. Each time he increased the dose he would feel sleepy, but this wore off after a couple of days. That was until, in February 2004, he reached 270mg – a dose 150-190mg above the maximum dose for most countries. At this level, the sleepiness did not wear off, but he noticed something else: his desire to drink had gone. "I was completely and effortlessly indifferent to it," he wrote.

He called this the "threshold dose" and reduced it until he came down to 120mg a day, a "maintenance dose" on which he remains to this day, occasionally topping up by 20-40mg when he feels particularly anxious. He can now even drink socially – an idea entirely counter to the teachings of AA and most other therapies. "I became disease-free," he says. It seemed he had discovered a treatment that might save millions of lives and improve those of even more.

This story raises many questions, the first of which – at least for an alcoholic – is: how come I don't know about this? "Well, that's the thing," sighs Ameisen. "It's exhausting." Naturally he wanted to share his discovery, even though to do so he would have to declare himself an alcoholic – something no practising doctor had done before. He wrote up his experiment for publication, as a "self-case report", and submitted it to the journal Alcohol and Alcoholism, published by the Oxford University Press. This appeared in December 2004 but barely caused a ripple. Unbowed, he circulated it to anyone who might have an influence. One of these, Nobel Laureate in Medicine Jean Dausset, told him he had discovered the cure for addiction but warned him: "Medical dogma can be slow to change." These would prove to be telling words.

It's not that there is much argument over how baclofen might work. Recent advances in brain imaging have increased knowledge of the function of the pleasure and reward systems, and suggested that addiction interferes with the balance of the neurotransmitters dopamine, glutamate and gamma- aminobutyric acid (GABA). "What baclofen does is stimulate the GABA-B receptors, and you see the release of dopamine and glutamate is slowed, so the reward system is normalised," says Ameisen. It is even widely accepted that baclofen in low doses treats withdrawal from alcoholism, though no more effectively than several other medications. What proved more controversial was Ameisen's theory of the "threshold dose", which he says is "needed to break the cycle of addictive craving, preoccupation and obsessive thoughts" and which moves baclofen from treatment to cure.

Ameisen was disappointed by the professional reaction to his discovery, but he found that potential patients were much more interested. Alerted by occasional mentions in the press, starting with a piece in Business Week in 2005, they began to contact him directly. Some eventually found an addiction specialist or GP willing to prescribe "off label" – to give them the drug for a purpose other than that for which it was intended and/or at a higher dose than recommended, at the doctor's risk. When, after two years of attempting to work within the medical system, Ameisen decided to go round it and wrote The End of My Addiction, published in France as Le Dernier Verre (The Last Glass), this process accelerated. Small groups of addicts using high-dose baclofen began to spring up around doctors who adopted Ameisen's ideas.

This is increasing "exponentially", according to Ameisen: there are 60 cases in Geneva, 50 in Ann Arbor, Michigan, 40 in Chicago, and so on. It's reached Britain, too, with 50 already in Glasgow and others around the country. One who followed his method was 51-year-old Debra, who had relapsed after almost five years' abstinence and was in a state she describes as "absolute bedlam. The first thing, as soon as I got up, was: 'How am I going to get my drink?'" Just after she'd discovered the book on Amazon, she visited her GP and he recommended trying the treatment. "I started on quite a high dose – 30mg in the morning, 30 at lunchtime and 40 at night – but it wasn't enough to get me off immediately. It's not a magic pill – my obsession with drinking was still so strong. It was once my mindset had changed and I'd opened up; baclofen in conjunction with really wanting to stop was when it hit home." After nine months, she says, "I have no cravings now."

Similar cases aren't hard to find. Another British patient who began taking the drug in April 2009 kept a detailed blog under the name Baclofenremedy. Though he started on 300mg – 30mg more than Ameisen's threshold dose – his early entries describe a cycle of relapse, anger, self-loathing, denial and despair that is a familiar tale for any alcoholic: "At 5am I drank six cans of beer, 3 San Miguel and 3 Gold Label, ******* idiot." About two months in, however, the tone changes: "I don't have to try and not have a beer, I just don't think about it the way I used to." Eventually, although his intention had been to drink "normally", he finds himself, just like Ameisen, totally uninterested in alcohol. "I just cannot picture [drinking]. It's like I don't agree with it any more personally," he writes.

Baclofenremedy's NHS GP did not wish to be interviewed for this piece, but confirmed that he had "prescribed baclofen at above maximum dose following Dr Ameisen's regime and that the treatment has worked very well for the one patient I have used it for". But not everyone can find a doctor who will prescribe the drug. Many alcoholics and addicts have taken to buying baclofen over the internet and conducting their own version of Ameisen's DIY treatment, exchanging information on websites such as the French alcool-et-baclofene.fr, the German baclofen-forum.com and English-language mywayout.org. This has gathered such momentum that Dr Fred Levin, professor of psychiatry and neuroscience at Northwestern Medical School, one of Ameisen's greatest champions and the doctor responsible for the 40 cases in Chicago, made it known on one website that he was willing to advise self-experimenters over the phone, out of hours, to ensure they treated themselves safely.

As yet, though it is increasingly widely accepted that all addictions and compulsive behaviours work on the same neurotransmitters, the use of high-dose baclofen on addictions to cocaine, heroin, nicotine or in eating disorders has not taken off in the same way. That said, Dr William Bucknam, the addiction psychiatrist in Ann Arbor, Michigan, who picked up Ameisen's method, counts cocaine addicts, smokers and binge eaters among the 50 he treats. There have also been positive studies on baclofen's effect on heroin in a 2007 Italian study, on cocaine in a small placebo-controlled trial at UCLA, California, in 2003 and on binge eating in New York and Pennsylvania in 2007, as well as several animal tests for cocaine, heroin, nicotine and dextroamphetamine.

These can be added to studies on alcoholics, most recently Ameisen's own, conducted on 100 patients over three months with Dr René de Beaurepaire of Le Centre Hospitalier Paul-Guiraud in Villejuif, near Paris, and published in February. This showed 88% either stopped drinking, regained control of their drinking or reduced it significantly, with thresholds reached at doses varying from 60mg to 300mg. These are significant figures, but it's clear, as it has been since Ameisen's self-case report was published, that until there has been a rigorously conducted double-blind placebo trial – a test whereby both the drug and a placebo are handed out at random, with neither patient nor doctor knowing which is which – few in medicine are going to take much notice.

For that, a number of factors would need to align. The first is funding, which would usually be provided by a drug company. The problem here is that baclofen is an old drug; although this means that Ameisen has been able to amass data from over 50 years' usage, it is also out of patent, and drug companies therefore have no incentive to trial it. And there's no shortage of drugs being trialled for alcoholism and addiction treatment that would bring profits. In February, Reuters reported 24 in development for alcoholism alone, while for addiction in general a 2006 piece in the New York Times said that America's National Institute of Drug Abuse was studying 200.

The second factor is the acceptance of the medical establishment. Ameisen has built up a network of supporters, some of them in senior, influential positions – Jerome Posner, chair of Neuro-oncology at the prestigious Memorial Sloan-Kettering Cancer Center, and Jean Dausset, for example. When we meet, he is about to fly to America to speak at the McLean Hospital Division of Alcohol and Drug Abuse of Harvard University, and reports on his return that they have "asked me to write them my protocol on a piece of paper, which I did, and that they will simply start prescribing". He has also been made a visiting professor at State University of New York which, as he points out, is "not out of charity".

But there are doubts. Even Professor Jonathan Chick, the Edinburgh-based psychiatrist who, as editor-in-chief of Alcohol and Alcoholism, published Ameisen's self-case report, is cautious. "It's a very moving, wonderful story, as indeed is his book," he says, "but we always have to realise in a single-case report there are factors that may be important that aren't necessarily being examined and therefore we can't conclude anything definite – for example, that the baclofen high dose made this remarkable change in him. One needs to conduct a randomised controlled study."

Professor Chick is treating 50 patients for alcoholism with baclofen, but not in the high doses of Ameisen's method; he stays within the maximum dose drawn up by the British National Formulary of 100mg a day. "We've been very encouraged by patients who had failed with previous attempts to abstain from alcohol who with baclofen have remained abstinent," he says. "We're not saying they've been cured for life; I don't think it's possible to say that. Professor Ameisen might say that we haven't used sufficiently high doses." And he is currently unwilling to go above the 100mg dose: "I do actually have some concerns about unwanted effects in larger doses. I don't want to give details to you – this is all rather provisional. This is a drug which is active in the brain, and there are concerns about some unwanted effects of higher doses in a very few people."

For Ameisen, this is a frustration. "In the nearly 50 years that baclofen has been prescribed, including at high dose – much higher than Dr Chick's maximum – I challenge you to find any report of any side effect that was severe or not reversible within 24 or 48 hours. Trust me, had there been one such report, I would have been demolished since 2004."

Ameisen has not hidden the fact that baclofen can have side effects, particularly if not managed properly, including sleepiness (or somnolence), dizziness, nausea, violent dreams, headaches and bouts of depression, or that sudden withdrawal is unsafe. He has also stated that: "No medication works effectively for everyone, and baclofen is surely no exception." With no official figures and many taking it without medical supervision, it's impossible to assess baclofen's success rate accurately. There's also no definitive way to measure success: anecdotal evidence suggests that those who don't achieve abstinence stop taking the drug because they find the side effects off-putting, and who's to say they wouldn't eventually have been cured if they had continued? "So far it seems to work in all types except for one," says Ameisen, "and that's people who turn up once and don't come again. But it's not one size fits all; you have to refine it. Not to say that I'm a great doc, but every time I'm on the case I've yet to find a patient where it's not a success. I've been playing with this medication for 10 years."

The miracle-cure aspect of the treatment has certainly provoked some addiction experts, though. In December 2008, for example, Dr Nicholas Pace, a clinical professor of medicine at New York University, told ABC News: "I have studied alcoholism for the past 40 years, and there is no single magic bullet. This is a complex disease, and you can't just flip one switch. The idea that an alcoholic can drink socially is simply a lot of bull." This kind of reaction, says Ameisen, comes from feeling threatened. "When you question a dogma, you're very vulnerable," he says. "People in the field feel stupid. The animal data was there for 30 years – I didn't invent this. I used a model; I did what they should have done." Plus, he says, "if baclofen works, then their specialism is going to fall apart. There are those who want trials to be blocked – it's not good for their business."

An alternative reason might be that they've heard claims like this before. Since the 1990s, several drugs introduced to treat alcoholism, such as Antabuse, Naltrexone and Campral, have proved disappointing. Before then, barbiturates, benzodiazepines such as Valium and antidepressants such as Prozac were each hyped as an end to addiction. In 2007, Prometa, a treatment for methamphetamine, alcohol and cocaine, was launched with claims of an 80% success rate but no double-blind testing, and was shot down almost at once.

Around the same time, ibogaine, a psychoactive substance used in African ceremonies, was hailed by a senior member of the American National Institute on Drug Abuse as the most promising anti-addiction medication he had seen, but has since been connected to 12 deaths. So when Dr Fred Levin said in April that "virtually every patient I've ever [treated with high-dose baclofen] has gotten well", it sounded too good to be true. As he said himself: "All of us in medicine are very sceptical when someone says something has approximately 100% success rate."

One psychiatrist I spoke to, who wished to remain anonymous because of his own alcoholism, told me: "There's been the emergence in the past few years of a number of drug therapies for alcoholism which are promising. But if you rated them on a level from one to 10, where 10 was 'complete cure' and 0 was 'doesn't work at all', most of the drugs in psychiatry are about 3 or 4, and drugs for addiction are more like a 2 or 3, or even 1 and 2. So anyone who insists that one of these medications is a wonder drug, a panacea or a cure, he probably has either got the patent for the medication or is trying to make a name for himself."

Ameisen has filed a patent application, but for "prevention of relapse on baclofen". He says this was solely to block rehab centres from doing so, and that he is dropping it because it is "costly and useless". Though he could have done so, he says, he never applied for a patent for his treatment.

There is also the question of whether a drug that you take for ever – the "maintenance dose" – is a cure at all. Ameisen says that the correct equivalent is a drug for high blood pressure or diabetes, but this might be questionable if there is always the option of "topping up", as when he says: "I sometimes think of alcohol and I take a pill and within 30, 40 minutes it's gone."

"'Whatever works' is my response," says Julian Keeling, a therapist with Tony Adams's Sporting Chance Clinic and a former drugs counsellor at Wandsworth Prison, "but there is the idea of taking a drug in order to come off a drug. There's a parallel with methadone, which I was on, a heroin substitute that has a much longer half-life and much less euphoria, so your life stabilises. It doesn't address underlying issues, though, and most people don't tend to destroy their life with alcohol and drugs unless they've got some fairly pronounced emotional disturbances that they're trying to escape from and medicate."

Could this attitude be due to the general acceptance that the 12-step programme and therapy are the treatment for addiction? Ameisen insists that his cure would not replace therapy or AA – "On the contrary, it will make all these programmes more effective" – but a medical cure would make AA, with its ideas of "defects of character" and "amends", seem like ancient superstition. "If I find a drug that works for me then I'm going to be psychologically addicted to it even if I'm not physically addicted to it, and it will do for me what I feel I ought to be doing for myself," says Keeling. "It's like that Louis Theroux documentary about medicated children: on the one hand, if you had a nightmare kid, why wouldn't you put him on Ritalin? But you look at it and some part of you says it's wrong. But do I have that reaction because I have a puritan view of medication due to 12-step brainwashing? I don't know."

As an addict, it's hard to decide about Dr Ameisen's treatment. Would I take it? Should I take it? Part of me – no doubt the part that has seen lives turned around in just that way – believes that Ameisen might have been able to recover with Alcoholics Anonymous alone. He says: "If someone managed through willpower to quit drinking, then great – he probably has something smaller than I had, because I was unable. Every disease has mild and severe cases – some people get the flu and die; some get it and don't even notice." He may well be right – I'd certainly agree he had (or has) it worse than me. But AA is based on surrender, on suppression of the ego and a very old-fashioned leap of faith; Ameisen found his cure through his refusal to surrender, listening to his ego, and through science. The problem is that science needs proof.

The End of My Addiction: How One Man Cured Himself of Alcoholism by Olivier Ameisen (Piatkus Books, £9.99) is published on 13 May

• This article was amended on 19 May 2010. The original stated that Olivier Ameisen is currently 57. This has been corrected.