The dangers of becoming addicted to over-the-counter (OTC) medicines are going unrecognised, doctors warn.
The researchers say more research is needed on how many misuse OTC drugs
In the British Medical Journal, Chris Ford and Beth Good say they have seen three patients addicted to drugs containing codeine in recent months.
All began using the drug as recommended, but their use grew.
The drug companies' trade association said there was guidance in packs, but researchers said the public needed to be more aware of the addiction risks.
All three of the patients seen by the doctors had been taking Nurofen Plus, a combination of codeine phosphate - which is an opiate - and ibuprofen.
They all had gastrointestinal bleeding, a side effect of excessive ibuprofen use.
One of the patients was taking 30 tablets a day - compared to the recommended maximum dose of six.
'Tip of the iceberg'
Alone, codeine phosphate is only available on prescription. But it has been available OTC in low doses and in combination with aspirin, paracetamol, or ibuprofen for many years.
The doctors say that the Over Count website highlights shows the most common addiction is to the OTC drug Solpadeine - a combination of paracetamol and codeine. The website suggests more than 4,000 people registered there currently have this problem.
But Dr Ford told the BBC News website she did not think the drugs were unsafe, or that they should be banned.
"Thousands and thousands of people take these drugs and don't have any problems. It's a very small minority who do.
"But our anxiety is that it's a problem which is not being picked up by the public or doctors, and that we're just seeing the tip of the iceberg."
Dr Ford added: "There are lots of websites where patients are talking about their addictions.
"But we have no idea how big the problem is because there has been no research to quantify it."
She added: "We need to get the evidence and also raise awareness in the general population and in the healthcare population."
The company which makes Nurofen Plus, Reckitt Benckiser said Nurofen Plus was sold under strict guidelines and was only available in 32 pill packs.
Packs also say patients should seek medical advice if they need to take the drug for longer than three days.
Dr Phil Berry, Reckitt Benckiser's global medical director, said: "There is a considerable body of scientific evidence illustrating the safety of OTC product combinations of codeine with either ibuprofen or paracetamol as long as they are used correctly for short term relief, according to the pack instructions."
A spokesman for GlaxoSmithKline, who make Solpadeine, said the company took reports of any OTC medicine misuse very seriously, but stressed it was rare.
He added: "Hundreds of thousands of people benefit from safe and effective use of Solpadeine every year.
"There are clear instructions for use on our labels, and if these are followed there is no evidence that the product will cause dependency."
Helen Darracott, of the Pharmaceutical Association of Great Britain, said: "OTC medicines which contain codeine or dihydrocodeine should be taken only to relieve symptoms of pain and only for short periods unless a doctor has advised otherwise.
"As with all medicines, people should consult their pharmacist or doctor if their symptoms persist or get worse.
"These medicines are already strictly regulated - they are only available from pharmacists and have clear instructions on how to use the medicine and when not to use the medicine."