At the time he said he was simply mentally and physically exhausted, prompting an array of conspiracy theories seeking the real reason for his departure days after his 60th birthday in 1976.
But according to The Independent, an analysis of his speech patterns has found that Wilson may have already been suffering the early stages of the disease which went on to destroy his prodigious memory and powers of concentration.
Dr Peter Garrard, Reader in Neurology at the University of Southampton School of Medicine, reports he has found a decline in mental function in Wilson's final months in Downing Street. He concludes that the onset of the disease could have contributed to Wilson's shock decision to step down as Prime Minister and Labour leader.
His research suggests that during his final months in office Wilson was losing his distinctive voice - seen as an indication the disease was beginning to have an impact on his speech patterns.
Dr Garrard's analysis have been published in the Journal of Neuro-linguistics.
Alzheimer's affects more than 400,000 Britons, and is the most common type of dementia. As it develops, the structure of the brain is attacked and the transmission of messages between different parts of the brain is impaired by a shortage of the right chemicals.
In the early stages, sufferers tend to have trouble remembering things and will often spend time searching for words. They may start substituting unusual or incorrect words for ones they have forgotten, or even invent new ones of their own. As the disease progresses, this forgetfulness becomes ever more severe and can lead to extreme confusion.
Consequently, people with the illness tend to become withdrawn as they lose their confidence in their ability to act normally. They often experience mood swings, feeling sad or angry about their inability to express themselves in their usual way.