They speculate that all three disorders may be caused by antibodies to the body's own nerve cells because of a mistake by the immune system following infection.
At the moment, the ultimate cause of these illnesses remains a mystery.
Writing in Medical Hypotheses, Dr Jim Morris from the University Hospitals of Morecambe Bay NHS Trust, Dr Sue Broughton and Dr Quenton Wessels from Lancaster University say current explanations are unsatisfactory.
"Psychological factors might be important, but are unconvincing as the primary or major cause.
"There might, for instance, be an increased incidence of physical and sexual abuse in childhood in those who go on to manifest functional disorders. It is easy to see how this could influence symptoms in adults but it stretches credulity to imagine abuse as the sole and sufficient cause of the functional disorder."
It is already well known that women are more at increased risk of autoimmune disease especially ones in which antibodies to the body's own cells are thought to play a role, like thyroid disease, pernicious anaemia and myasthenia gravis.
The researchers said: "The female to male ratio in these conditions is of the order of 10. The female excess in Irritable Bowel Syndrome, Chronic Fatigue Syndrome and Anorexia Nervosa is equally extreme and therefore this fits with the idea that auto-antibodies to nerve cells could be part of the pathogenesis of these conditions."
The formation of auto-antibodies is found mostly among women and increases with age, which could be why these disorders are more common in midlife. Even with anorexia, which reaches a peak at the age of 30, auto-antibodies have been found in the bodies of patients.