All three had started taking the drug for its approved benefits, but their use increased as they became tolerant to the codeine element.
Although codeine phosphate is only available on prescription, people can buy it in combination with aspirin, paracetamol or ibuprofen.
Dr Beth Good and Dr Chris Ford argue that the three people seen by them are indicative of a wider problem in OTC drug addiction in the UK.
Their search of the online research database MedLine found that no studies have been conducted into OTC drug dependence in the UK, but after trawling the internet they came across numerous sites offering support to those addicted.
These "tell many personal stories, often remarkably similar and usually starting with appropriate use of analgesia [painkiller] for pain such as back injury or menstrual cramps," Drs Good and Ford found.
The most common addiction appeared to be to Solpadeine (paracetamol and codeine) – one site alone had 4,000 people registered as having this problem.
"There are no official statistics documenting the extent of dependence on legal non-prescription drugs," the doctors conclude. "We need large scale research to assess and monitor the extent of the problem."
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.