In the field of "positive thinking", the world's most influential guru is a prim silver-haired 86-year-old woman called Louise Hay.

Hay – once described by the New York Times as "The Queen of the New Age" – wrote a book called You Can Heal Your Life in 1984. To date, it has sold 35 million copies. She went on to found Hay House, a self-help publisher which now has an annual turnover of £35 million. She also claims to have healed herself of cervical cancer, mainly through the power of thought.

Today she is headlining a self-help conference at the SECC in Glasgow called I Can Do It!, billed as "the greatest motivational and inspirational event in the world". She is appearing along with a host of other "gurus", many of whom buy into her belief that illness is the product of our thoughts, and that healing is just a matter of reworking those thoughts.

The event, run by Hay House, has sold out, with thousands of Scots pouring through the door having paid up to £299 a ticket.

Among the other speakers are Wayne Dyer, who has chronic lymphotic leukaemia but deals with his condition by repeating the mantra, "I am well". There is also Anita Moorjani, who was told in 2006 she was just hours away from death with terminal cancer, before she had a spiritual experience followed by "a total recovery of her health".

These people are at the centre of a disturbing approach to illness, and cancer in particular, that sees it as a disease to be tackled with the mind and positive thinking.

It is a movement which many within the medical establishment believe is dangerous.

Cancer Research UK's head information nurse, Martin Ledwick, says: "We would strongly advise people not to use a positive mental attitude as a substitute for treatment. There's no scientific evidence that being positive can improve survival in cancer patients."

They are not alone in their scepticism. High-profile American oncologist Siddharta Mukherjee, author of The Emperor Of All Maladies, has said: "A positive mental attitude does not cure cancer any more than a negative mental attitude causes cancer."

Dr Peter Allmark of Sheffield Hallam University, co-author of a 2011 paper, A Critique Of Positive Thinking In Cancer Care, denounces the approach as "quackery".

He notes that "the danger of these things is that people will perceive this as an alternative to conventional medicine" and urges those diagnosed with cancer "not to reject anything in terms of conventional care".

He also says that even the assumption that positive thinking at least cannot do any harm may be wrong: "There is research showing that people can be harmed: by the pressure they feel when they get cancer that you either have to be a hero or a victim and you can't just be someone who is really angry or all the things that you might feel."

Allmark also dismisses the examples that Hay and others like her use to support their ideas, saying: "Hay is part of the alternative new age movement and they tend to report mainly on anecdotes of people saying, 'I've survived' or, 'Positive thinking changed my life'. This leads to a reporting bias. People who don't survive don't come and give you anecdotes."

Self-help is a huge industry, especially in publishing, and many see gurus like Hay as charismatic, living tributes to their philosophy – and thus powerfully persuasive. Hay, for instance, is a warm, engaging octogenarian, who recommends touchy-feely therapy like "mirror work", which involves looking at your own reflection and saying, "I love you" every day.

Hay reports that she was diagnosed with cervical cancer in 1977 and concluded that it could be attributed to holding on to her resentment for childhood abuse and rape.

She refused conventional medical treatment, and claims to have rid herself of cancer through thought, nutrition and alternative therapies. When she was diagnosed, she had for some time been a workshop leader in Religious Science, a church which follows new age beliefs, and published the pamphlet Heal Your Body, which contained a list of illnesses and their "probable" metaphysical causes. The cancer, she says, did not recur, nor has she had any major health problems in the 35 years since.

Another speaker at the SECC conference is Wayne Dyer, 72. He announced three years ago that he had been diagnosed with chronic lymphocytic leukaemia. Now, when he arrives on stage, he introduces himself and then says: "I am well." He repeats that phrase in a phone call to me from his home in Hawaii, and adds: "I am in perfect health." It is what he says when he meditates. His form of cancer is one with a slow progress rate, and which is most common in people over the age of 60. When he announced the diagnosis, he described it as a "great blessing in my life".

Dyer says he no longer visits a doctor or pays attention to blood count numbers.

He adds: "Honestly, I don't believe the cancer does exist any longer. I stopped going to the doctors when I had a [spiritual healing] and everything changed. I decided to live my life on the basis of how I feel. The other thing is I'm not afraid of death at all."

The "New Thought" movement, as it is often called, is not only untroubled by criticisms from the field of medicine, but it also believes that there is an increasing body of scientific research to support its claims. Indeed, there is a whole burgeoning industry in books on this subject. Dr David Hamilton, a Scot and former pharmaceutical scientist speaking at the I Can Do It! conference this weekend, is an author of works including The Contagious Power Of Thinking: How Your Thoughts Can Influence The World, and How Your Mind Can Heal Your Body. It is a sign of the huge interest in the self-help industry that he currently does 150 speaking engagements a year.

Hamilton, however, is always at pains to emphasise that he believes positive thinking techniques should be used alongside conventional medicine. "The first thing I say to people is, 'This doesn't mean you use your mind instead of medical advice. You use it as well," he says. "Most oncologists like the fact that I say, 'Please take your medicine'. If I had cancer I would take chemotherapy. But I would also change my diet, do visualisation. I would make the lifestyle changes in addition to, not instead."

He notes one shift that has occurred is that some parts of the scientific establishment have started to take seriously the idea that the mind can have an impact on physical health.

Hamilton says: "One of the things that has helped push this as an area of research is the development of MRI scans. A few decades ago there was such a belief everything was caused by brain chemistry. But now we see, from looking at these scans, that if you can change the thinking, you can change the brain chemistry. This would have been heresy a few decades ago."

Hay says: "I do not need scientific anything. If it feels right, then it's right for me. But there are many, many people who will not touch anything that doesn't have some scientific proof; I think it will enlarge the audience."

The extent of Hay's influence is huge. Almost everyone in the field of positive thinking or "New Thought" has read her books. One of Scotland's leading spiritual guides, Kyle Gray, who styles himself as an "angel whisperer", says he has every Hay book.

He notes how mainstream her ideas have become. "Twenty-five years ago, Louise first started to put her ideas out there. A lot of people thought it was really rubbish. But now it's fairly mainstream. The New Thought ideas have become accepted. It's not looking like witchcraft."

Hay House has long been a big player in an industry that, in these times of recession, is in boom. In Scotland in the last year, sales of self-help books were up 15%, while other book sales were down.

As Scottish life coach Ali Campbell – often referred to as "a guru to the stars" – puts it: "People are looking for answers and people are in pain, and when you're in a situation where everything that you thought you knew was actually up for debate, of course one of the cheapest ways to get help is to pick up a book."

A backlash is growing against positive thinking, however – particularly in relation to cancer. Books like Steve Salerno's SHAM: How The Gurus Of The Self Help Movement Make Us Helpless; Barbara Ehrenreich's Smile Or Die: How Positive Thinking Fooled America And The World; and Oliver Burkeman's The Antidote, are part of that counter strike.

More importantly, scientific research suggests the effects of positive thinking on cancer survival are not significant.

Ten years ago, Professor Mark Petticrew of the London School of Hygiene & Tropical Medicine found "little consistent evidence that psychological coping styles play an important part in survival from or recurrence of cancer".

Following the publication of his paper, he says he received "very moving personal letters from both patients and their families, in the UK and elsewhere, saying that they found the review helpful, because they felt oppressed by the pressure to "think positively" and "fight cancer".

Joanne V Wood of the University of Waterloo in Canada researched the effect of self-affirming mantras. She found: "Positive self-statements do not work for everyone. They may give a bit of a boost for people with high self-esteem or who are already confident, but our studies showed that for people with low self-esteem, repeating the phrase, 'I am a lovable person' made them feel worse, not better."

Psychologist and author Oliver James describes this "law of attraction" strand of self-help – the idea that you can bring good things to your life simply by willing them – as "snake oil".

To be fair, none of the gurus in Glasgow are actually telling people to give up on doctors and stop taking the medicine, whether it be chemotherapy or painkillers.

Wayne Dyer says: "I don't put down medicine. Our life expectancy has extended by 30 years, and that has a lot to do with modern medicine.

"I just think that the focus is on surgery and drugs and we've become much too focused on these things."

However, their own stories are an example and send out a clear message: even if we don't read their books or attend their courses, somehow, in some way, we should be thinking ourselves better.