The Viva Mayr clinic, a functional-looking alpine lodge, overlooks Lake Altaussee in Austria. Here a very famous supermodel once took off all her clothes and lay down naked on the banks, toes in the water, apparently in an “extreme emotional state”. The witness, another patient at the clinic, explained that this was not an abnormal reaction to day three at the Mayr.

Viva Mayr is a health centre that specialises in a form of extreme detoxification it refers to as “the Mayr cure”. Patients consume around 600 calories a day – roughly equivalent to one Pret a Manger BLT sandwich. But there’s no gluten here. Even grapes are vetoed. Epsom salts, water and goat’s cheese (lactose-free), however, are central themes. The programme is as notorious as it is successful (Vogue staffers and oligarchs are among the clinic’s regulars), and it’s generally booked up all year.

The idea is that patients will spend one life-changing lakeside week there and return home, revived, reborn, re-educated and, crucially, thinner. In fact, a loss of appetite – along with severe headaches and lengthy bouts of crying – is apparently par for the course, particularly on the third and fifth days, presumably thanks to the stomach massages, blood tests and chewing lessons in which the clinic specialises.

Still, it certainly seems to have its fans: Michael Gove is said to have lost two stone here. The Rolling Stones are repeat visitors, model Karlie Kloss has been, Suki Waterhouse spent a summer holiday there and Tracey Emin reportedly stays every autumn (and can often be spotted taking fag breaks). Two of the most popular diets of the last decade – the 5:2 fasting regime and the alkaline plan – first found fame at Mayr. It also supposedly inspired the “Hoffler Klinik” in the last Bond film, Spectre. This form of extreme health is even proving popular among the Trump cabinet. At last month’s G20 summit, US secretary of state Rex Tillerson stayed at the Steigenberger Sanatorium, a private clinic outside Bonn known for its naturopathy treatments. He claimed all the hotels were full.

And now Mayr is coming here. At the start of April, it will open in London. The first month is already booked up. A few years ago, they tested the waters with a £950-a-go clinic at the Corinthia, a five-star hotel in Mayfair frequented by Rihanna, which tells you something about their target market. But this is the first of their foreign outposts (they have also cropped up in Istanbul, New York and Athens) to focus primarily on health rather than the “spa” element. The day clinic will test your alkaline levels, your blood and even your stress levels. Consultations start at a princely £170.

I spoke to a private GP – a former client who once started up her own practice in London in tandem with Viva Mayr, and wished to remain anonymous – about its success. She believes it is in part thanks to the method of diagnosis favoured at the clinic. They use applied kinesiology (AK), or basic muscle testing, for evaluating “areas of dysfunction” – if they think you’re lactose intolerant, they pop lactose on your tongue and measure your muscle reaction. It is, however, a controversial technique: “It’s commonplace in Austria, but in the UK we’re suspicious of it.” The clinic maintains it is used by many professions.

“The problem is that AK doesn’t have any scientific basis as such,” explains Dr Benn Gooch, an NHS GP, “so I would be cautious about any diagnoses made using this technique. I would take it with a pinch of salt.” Gooch is wary of the so-called “Mayr cure”, especially the controversial idea that eating alkaline foods can give health benefits. “But with regards to functional symptoms, things like chronic pain and fatigue, they may be amenable to massage and this sort of treatment. It all sounds rather relaxing, and a good holiday has obvious benefits, but I’m not sure it can claim anything more than that. The Mayr cure is a treatment for the malaise of opulence more than anything else.”

The “Mayr cure” was developed almost 100 years ago by Dr Franz Xaver Mayr, an Austrian physician who believed in “auto-intoxication”: the idea that we are poisoning ourselves by ingesting the wrong things, which we then struggle to get rid of. “Everything starts with the gut,” explains Dr Christine Stossier, assistant medical director of the clinic. She and her husband, Harald, opened Viva Mayr in 2005, basing it on the practices of the original FX Mayr health centre, which opened in 1976. “The fundamental principle is that you can improve someone health’s through digestion,” she says. Our bodies are ill-equipped to deal with what we eat, she argues – namely the quantity of “gluten, manipulated dairy and low-fat foods” – but more importantly, perhaps, the way we eat it: “quickly, as snacks, with little variety and, when we eat in restaurants, without much attention to the freshness of our vegetables”. It’s not, she says, that she is treating patients with allergies; rather, she is focusing on things at the “groundwork” stage. “You can eat healthy, organic food, but if you eat it in the wrong way” – without chewing at least 30 times per mouthful; no raw food after 4pm – “it loses a lot of its value.” An NHS doctor I spoke to thinks this is dubious: “I cannot see any value in timing food preparation technique with particular times of day,” he says.

A few years ago, I went to the Adler Thermae spa in Tuscany, an offshoot of Mayr. It’s less dogmatic but they instructed me to avoid lactose and drink three litres of water a day. Doctors gave me salts to drink and I went to bed hungry. But, being in Italy, I was still allowed to drink coffee. Mayr’s aim isn’t solely to lose weight, but I lost two kilos in three days. My energy levels were markedly higher, though that might have been due to extra sleep, and my eyes turned strangely white. But for those with a fixed income, a job, or a life, it all felt untenable. Extreme diets are two-a-penny, and a recent study from the University of Melbourne found that elimination diets aren’t much better than calorie-controlled ones in terms of results. Dr Stossier uses the word “cleansing”, yet the principles of mindfulness and fasting are similar. Whether this works because of the diet, or because you are alive and have a liver, is a moot point.

Mayr is viewed by many as a last straw, an outrageous luxury and proof of the survival of the richest. Others swear by it. In reality, a lot of clients are simply suffering from chronic fatigue, and need a little TLC – healthy food, fresh air and sleep. “I have a friend who goes to the Mayr clinic every year for 10 days,” says the private GP. “He drinks and smokes and says he would be dead by now if he didn’t go. What more of a reason does anyone need?” Perhaps. But it’s a triumph of marketing, too.

• This article was amended on 27 March 2017 to remove a name