There is a classic Mitchell and Webb sketch in which two doctors working in a “homeopathic A&E” treat a patient who has just been hit by a car. “Get me some wolfsbane, also known as monkshood, in here!” shouts Webb over the gurney. “And a whole tray of flower remedies!” Mitchell winces: “Oh … his chakras are fading. He needs some crystals.” Webb responds: “Nurse – fetch me some purple-tinted quartz! All right, make that aquamarine quartz!”

The dialogue is as funny as it is because it parodies a form of delusion and superstition that – far from fading – is gaining traction at a deeply alarming pace. Pseudoscience is nothing new, but its scale and proliferation most definitely are. And the consequences are real and frightening (full disclosure: I am a trustee of the Science Museum Group). Last week, a study by scientists at Yale University of 1,000 patients with breast, prostate, lung or bowel cancer showed that those who used so-called complementary treatments were twice as likely to die as those who did not. The study, published in the journal JAMA Oncology, concluded the primary reason for this was that the subjects seeking “alternative” cures were more likely to delay or refuse conventional cancer therapy.

Meanwhile, it has been reported that Andrew Wakefield – a disgraced doctor whose claims that there is a link between vaccines and autism have been comprehensively and repeatedly discredited – is dating Elle Macpherson, an Australian businesswoman and supermodel. Though not of much scientific importance in itself, this liaison symbolises the appalling success with which Wakefield has turned his academic infamy into a form of celebrity. Struck off as a medical practitioner in the UK, he has reinvented himself in the US as a populist guru and protector of children, fighting the wicked establishment of the pharmaceutical companies, government and supposedly corrupt doctors.

The extraordinary spread of pseudoscience chimes with the spirit of the age: expertise, once a claim to authority, is now often regarded as a liability. The medical research community is increasingly distrusted as just another mendacious elite seeking to control the more open-minded public. Not surprisingly, social media has been the principal engine of change, weaponising bogus medicine, fakery and charlatanism of all sorts. Conspiracy theorists scuttle over the web, encouraging disdain for conventional medical practice and (most recently) alleging that what we call science is just another western “social construct”.

And fighting back is not straightforward. William Davies argues in his brilliant forthcoming book, Nervous States: How Feeling Took Over the World: “Phoney science can be demolished. The problem is, it takes time.” The scientists are making a complex case, the pseudoscientists merely mobilising opinion and appealing to public sentiment by digital means.

I don’t want to close down spas, ban herbal tea and charcoal balm, stop people buying botanical products or enjoying reiki. Many modern pharmaceuticals have their roots in ancient herbal treatments: the precursor to aspirin, for instance, was found in willow tree leaves. But as Tim Minchin has joked: “Do you know what they call alternative medicine that’s been proven to work? Medicine.”

Once again, the gag captures a genuine peril. What so many pseudoscientists and champions of “complementary medicine” do is to undermine trust in treatments that are actually effective – with terrible real-life consequences. Since Wakefield’s campaign began, the incidence of measles has risen appallingly, with many losses of life. The Yale study should give pause to every person who, hearing that a friend or loved one has been diagnosed with a tumour, is minded to send them a leaflet about an amazing new diet, or tell them a story about the aunt of a neighbour of a colleague who was “cured” by a shaman in Streatham.

It is a particular irony in the case of cancer that, precisely at the moment that pseudoscience is on the rampage, we stand on the brink of a historic breakthrough in oncology. I recently met a cancer specialist who refers to himself as an “algorithmist” because his work entails the development of super-specific drug treatments, computerised protocols based on genetic mapping. Immunotherapy and related practices should soon turn what is all too often a terminal disease into, at worst, a chronic condition like diabetes. It is hard to exaggerate the potential benefits to humanity that may lie in the not-too-distant future.

The catch, of course, is that such treatments will require funding, and lots of it. But researchers I have spoken to say the challenge will be one not only of regularised resources, but of public education. A decade from now, the traditional trinity of surgical resection, radiotherapy and chemotherapy will look very old-fashioned. As cancer treatment becomes more complex – a lot more complex – it will be ever more important that patients have some idea of how to navigate these new shoals.

Yet modern culture loathes complexity. Populism – the claim that there are easy answers to difficult problems – is surging around the world. Build a wall, leave the EU, ignore doctors: this is the high season of snake-oil salesmen selling bogus tonics off a cart to punters who crave an easy solution to problems of great subtlety and nuance. The desire for simplicity is a natural human instinct. Confronted by the kaleidoscopic multiplicity of contemporary life, we heed those who promise to make everything better with the flourish of a wand. But one of the tasks of true leadership – in all fields – is to explain that simplicity is not always possible, decreasingly so.

It is part of the maturation of our species that we accept that immigration is not the cause of our social ills, that the Earth is not (as a growing number of people believe) flat, and that carrot juice absolutely cannot cure cancer. It is time to put aside childish things.

• Matthew d’Ancona is a Guardian columnist