In a climate that often feels hostile to middle-aged women, maybe it’s a sign of progress that an only faintly convincing contribution on menopause management can become, as one did last week, a cause for national rejoicing.

That’s if it doesn’t just confirm suspicions that, where women’s health is concerned, any visionary, antique or drug-repudiating theory can still become mainstream. So long as NHS clinicians congratulate women for enduring, say, medieval-style childbirth, maybe it isn’t surprising to find an appreciative audience for a new study advocating, for hot flushes and other menopausal symptoms, cold-water swimming: therapy not strikingly advanced from the cold-bathing regime propounded by a Sir John Floyer in 1702.

Given the warm media response, joy at Dryrobe’s HQ must have been unconfined. Could cold-water bathing, if it can’t entirely dislodge the pharmacopeia, progress from fashionable hobby to routine social prescribing? If menopause-afflicted women can be persuaded to set off, in their millions, in search of immersion-quality freezing water, why shouldn’t this treatment work for equally distressing symptoms – assuming they exist – for which effective relief is also available but often so grudgingly dispensed?

The finding in a new study from UCL’s Elizabeth Garrett Anderson Institute for Women’s Health that swimming in cold water appears to ease menopausal symptoms – at least among women who love swimming in cold water and are lucky enough to find some with no sewage in it – became national news beneath headlines significantly more ambitious than the study’s title (“How do women feel cold water swimming affects their menstrual and perimenopausal symptoms?”). “The benefits of cold water swimming on menopausal symptoms” was one; another, “Going for a cold water swim ‘can combat symptoms of menopause’ ”, was accompanied by the bullet points: “Researchers in London found nearly half said it improved their anxiety”; “Almost a third also reported it helped their low moods and hot flushes”.

A half of who? A third of how recruited? What were their symptoms when they began swimming? Were any participants also taking established hormone replacement therapy (HRT) proved to help with hot flushes and other menopausal symptoms? Or indeed, any of the non-evidence-based products, Goopish and worse, which now contribute to a global menopause industry estimated at $16.93bn (£13.3bn)?

Only a few respectful reports about what proved to be a study with no control group featured the still less convincing detail that it was based on self-reporting by enthusiasts responding to ads on cold-water swimming groups on Facebook. That is, it drew, though more extensively, on the sort of personal avowals currently enraging Dragons’ Den viewers.

It would have been remarkable, in fact, given the attractions of outdoor swimming, social, aesthetic and physical, if these regulars had not reported positive outcomes to a study apparently so keen to elicit them, whose senior author, keen outdoor swimmer Professor Joyce Harper, appears to be UCL’s answer to John the Baptist. “The exhilaration when the water is cold is amazing,” she writes elsewhere, uninspiringly to anyone who considers this particular activity, if not actually hellish, impracticable for most urban dwellers in a country where bathing water is increasingly replaced by excrement. To be fair, listed under various limitations in Harper’s study, is the observation that other outdoor activities might offer similar benefits. “It is likely,” the authors say, “that we would get similar results for women who do other sports in nature such as paddleboarding, kayaking and sports that were not so risky, such as walking.”

Maybe walking would actually be a safer bet? On the day the swimming-menopause study came out, London’s City Hall calculated that Thames Water quadrupled its sewage dumping in the last year, up to 6,950 hours. But Harper’s research, though it mentions the risk of gastroenteritis, still favours cold-water swimming over less dashing but possibly more user-friendly exercise. The hope is, the authors say, “in the light of the benefits our participants recorded, [to] increase the number of women partaking in this activity”.

In terms of objective value, you could compare the study with one asking, say, regular attenders at a model railway club if they find their gatherings alleviate low mood in middle age. With the difference, of course, that results testifying to the participants’ genuine euphoria would probably never make it into a GP’s consulting room. Which cold-water swimming almost certainly will, now. Even recent history indicates that, where menopausal symptoms are involved, any not-completely-insane, non-pharmaceutical solution can end up being suggested to women in lieu of causally directed medicine, whether it’s by a GP or another supposed menopause authority.

News of the UCL cold-water cure arrives just two months after women discovered that the National Institute for Health and Care Excellence, reviewing treatment of menopausal symptoms, proposed, to the consternation of some campaigners, using cognitive behaviour therapy to treat conditions considered “bothersome” (a clinical term still favoured for female distress resulting from hormone deficiency). The campaign group Menopause Mandate objected, among other things, to “vague and patronising” language.

Others noted limited enthusiasm for the most effective treatment for menopausal symptoms, HRT, which can be traced back to a now discredited 2002 study that dramatically misrepresented its risks, precipitating a steep decline in both prescribing and acceptance, and leaving lingering suspicion and misconceptions. The CEO of Mumsnet, Justine Roberts, said: “Women already struggle to access the HRT they are entitled to. We hear daily from women in perimenopause and menopause who are battling against a toxic combination of entrenched misogyny, misinformation and lack of knowledge among GPs.”

Which is not to say that women’s recourse, as an alternative, to icy, turbid water could not have unintended benefits. A great army of bothered women, energised by regular immersion, could yet be the avenging tide our water companies deserve.

• Catherine Bennett is an Observer columnist