In Boots, Tesco, Superdrug and branches of Lloyds pharmacy you see them, marketed like sweets with brand names that leave no ambiguity about their purpose: Smartfish, eye q chews, Healthspan Brain Boosters, Boots Smart Omega 3 Fish Oil, Valupak Smart Omega 3 in Honey. Every year, we in Britain spend £116 million on fish-oil supplements (twice the amount we spend on over-the-counter hay-fever treatments) in the belief that the omega-3 fats they contain boost our children's intelligence - yet, to date, not a single study has shown that omega 3 improves brain function in the general population.

If ever there was a breach of advertising standards, this, one might think, is it - yet such names are legal because they don't amount to a 'claim', a statement of health benefits that cannot be made without medical consensus.

Dr Alex Richardson, a senior research fellow at Oxford University and an authority on nutrition and the brain, is baffled by the loophole. 'Nobody has yet done a trial that looks at unselected children,' she confirms. 'Studies have focused on kids with specific difficulties,' she adds, referring to the handful of small but properly controlled trials that have taken place - using children with ADHD, dyslexia, dyspraxia and developmental coordination disorder (DCD). Of these, three showed slight improvements in children who took the fish oil, and two didn't - hardly a ringing endorsement of omega 3 as a brain food.

The largest experiment, the Oxford-Durham Study, was conducted in 2002 by Dr Richardson herself, who gave fish-oil capsules to children with DCD - a disorder affecting motor coordination, learning and social or psychological adjustment. In its wake came further 'Durham trials', all overseen by Dr Madeleine Portwood, an educational psychologist employed by Durham Local Education Authority, who had worked with Dr Richardson on the first trial.

'They hijacked the phrase,' Dr Richardson maintains, 'and there was a new supposed Durham trial every two minutes, all engendering confusion.' Crucially, only one used a control group (children who were not taking the fish oil, in order to make comparisons) and a placebo (dummy fish-oil capsules), and none was conducted double-blind (where neither the researchers nor the children know who has taken the pills) or has ever resulted in a published, peer-reviewed paper. In one, pre-school children were given a supplement and their behaviour was assessed by their parents.

In the most controversial example, Equazen - the manufacturer of eye q fish-oil supplements - was approached by Durham LEA and asked if it would donate £1m-worth of capsules to be doled out to 5,000 school-age children in the run-up to their GCSEs. Their performance will be measured against what it might theoretically have been without the omega 3. Again, there is no control group, no placebo and no double-blind component.

Despite such blatant flaws, these 'trials' were widely reported, invariably mentioning the eye q brand and declaring fish oil a wonder supplement. In December last year, Equazen was sold to the Swiss pharmaceuticals giant Galenica, making a reported £10m-£20m for its chief executive Adam Kelliher. Only Ben Goldacre of the Guardian reported the debacle for what it was in his Bad Science column, and this led to further media exposure of the Durham project.

'This is not science,' said Professor Tom Sanders, an expert in nutrition at King's College London, at the time. 'Studies that are uncontrolled undermine properly conducted research and bring a lot of discredit to the scientific community. Parents are being seriously misled if they think they are taking part in a trial showing that fish oil will improve their children's performance.'

Nevertheless, hardly a month goes by without another 'trial' breathlessly reported by newspapers: in Bradford, pupils at Newhall Park Primary School were given omega 3 and '81 per cent showed improvements in reading, 67 per cent in writing and 74 per cent in maths', wrote the Independent - but again without proper controls and based on anecdotal evidence. In March this year, the Times reported 'astonishing' improvements in concentration, reading and memory in obese children who took a supplement called VegEPA. 'That study was based on four children,' says Dr Richardson, with no control group, the supplement named right in the middle of the article - and the only publication was pending.'

Yet the omega-3 bandwagon rolls on. Recently Premier Foods launched a baked-bean brand called Branstein -'the smart choice for parents who are keen to get more of the goodness of omega 3 into their kids', says Rob Stacey, marketing manager for Branston. A 210g serving provides 17 per cent of the recommended daily intake of omega 3 and an entire tin 34 per cent, but the company has been careful not to make claims about intelligence. Only the brand name hints at it.

Aimed at children who won't eat oily fish, Branstein is just the latest attempt to insinuate omega 3 into their diets by stealth. St Ivel Advance (or 'clever milk', promoted in an ad campaign fronted by Professor Lord Winston) is also fortified with omega 3. In June 2006, its manufacturer - Dairy Crest - was forced to withdraw advertisements after an adjudication by the Advertising Standards Authority, saying the claim that 'more omega 3 may enhance some children's concentration and learning' breached six clauses of the ASA code of practice and was misleading. Ironically, one of the complainants was Equazen, manufacturer of eye q pills.

Despite such stumbling blocks, omega 3 is big business. Frost & Sullivan, the global research consultancy, estimates that the market for omega-3 products (worth £116m in Britain) will grow by eight per cent a year until 2010. Datamonitor, another research company, identifies it as one of the 'big four' health-and-wellness trends in the packaged-food industry next year. At the same time, 25 European governments are funding the Lipgene project - a five-year study examining ways of modifying foods to contain more omega 3.

'They're looking at foods we commonly consume, such as meat, milk and yoghurt,' says Dr Joanne Lunn of the British Nutrition Foundation, a partner in the project. 'That way, we won't have to make huge dietary shifts because, if you tell people to eat more oily fish, they won't.' Genes which convert plant omega-3 into the EPA and DHA types found in oily fish and seafood (the easiest for the body to use) are being inserted into rapeseed, a crop used in cereal feed for livestock.

At the University of Missouri, scientists have created transgenic pigs that can break down omega-6 fatty acids (which are common in our diet) into the long-chain omega-3 versions (which aren't). This they have done by inserting a gene from a roundworm, transforming bacon into a 'brain food' that children might actually eat. The biotech companies DuPont and BASF are engaged in what they call a 'fish-oil arms race' to derive omega-3 fats from soybeans, linseed and brassicas rather than fish, which is a dwindling, unsustainable resource due to overfishing. Their efforts have been hampered by technical problems.

It's a brave new world of agrotech madness, but why are companies - and governments - doing this? First, scientists are pretty much agreed (with the exception of one negative, much-criticised study, published in the British Medical Journal last year) that long-chain, omega-3 fatty acids have a protective effect on the heart - and it is legal to make claims about this on packaging. Lipgene researchers think omega 3 could also combat the rise of 'metabolic syndrome' - a combination of type-2 diabetes, abnormal blood lipids and high blood pressure that is expected to affect 31m Europeans by 2010. 'We are eating too many saturated fats and not enough long-chain, omega-3 polyunsaturated fats,' says Dr Joanne Lunn. 'By manipulating the fatty-acid profile of the diet, we could improve public health outcomes.'

Second, while there is no robust evidence that omega 3 boosts intelligence, there is no doubt that these liquid omega-3 fats keep the brain lubricated and working properly. Since 65 per cent of the brain is made up of EPA and DHA, it makes sense that we require them in our diet. 'There is pretty compelling evidence now that a low intake of omega 3 contributes to just about every physical health condition, and probably mental health condition as well,' argues Dr Richardson. 'It genuinely is a critical nutrient for brain function.'

There are promising signs, for instance, that omega 3 may slow the onset of age-related memory decline as seen in early-stages of Alzheimer's, and three trials are under way on this - including one by the Food Standards Agency. In a recent study in the Lancet, women who exceeded the recommended intake of oily fish during pregnancy (two 140g portions a week) had children who did better in areas ranging from verbal intelligence and motor skills to pro-social behaviour. In depressed adults, a gram a day of EPA or DHA (recommended by the American Psychiatric Association) can significantly reduce symptoms.

'On current evidence,' Dr Richardson suggests, 'fish oils might be at least as much help in alleviating anxiety, stress and depression in all those worried mums as they are in improving behaviour and learning ability in their children.'

The trouble is, fish-oil supplements don't have nearly as much clout as oily fish - the mackerel, sardines, salmon and fresh tuna (canned tuna is less beneficial). 'Studies have shown that you need incredibly high doses of omega 3 given as a pure fish-oil supplement to get the same effects as with oily fish eaten regularly in the diet,' says Anna Denny, a nutrition scientist with the British Nutrition Foundation. 'The chances are, there is something else in oily fish that works in synergy with omega 3.'

Dr Richardson agrees: 'There is no question, you'd do better eating the whole fish. We always absorb nutrients better when they're packaged in the form that nature provides; that's what we are evolved to use. There are also other nutrients you'll get from oily fish which you're not going to find in a capsule.'

Unfortunately, advice given in the past about alternative sources of omega 3 (flax, hemp, sunflower and pumpkin seeds, and their cold-pressed oils) is rapidly losing credibility. Plants are a source of alpha-linolenic acid (ALA), another 'healthy' omega-3 fatty acid that is broken down by the body into the required EPA and DHA.

'The amounts we can synthesise from ALA are absolutely pitiful,' Dr Richardson warns. 'You can give pregnant women 20g a day of flax oil and you will change the DHA content of their breast milk not one iota. That study has been done. So all the people making fortunes flogging flax oil because it's got wonderful omega 3s, are just riding on the brain benefits, the heart benefits [of EPA and DHA]. It's even more of a hype.'

With the new generation of omega-fortified foods, it is vital to study the label and make sure the omega 3 really is EPA or DHA. Next, Dr Richardson says, check the amount - 'and think of your target as half a gram a day for a healthy heart'. St Ivel advance milk, she adds, does contain the right EPA and DHA - 'but as for getting your half a gram a day from that alone, you won't. You'd need about three litres of the stuff to get anywhere near it.'

In short, you can give children omega-3-fortified orange juice for breakfast, omega-3 bread and Branstein beans for tea - but there is no substitute for oily fish twice a week. Studies have also shown that organic milk and suckling Swaledale lamb, reared only on milk and grass, have higher levels of omega 3 than conventional milk and lowland lamb.

However, what we subtract from the diet may be as important as what we add. The World Health Organisation recommends a 2:1 ratio of omega 6 (found in cereals, meat and milk) to omega 3 for optimum brain development, and 5:1 for general health. 'These days it is more like 15:1 in favour of the omega 6s,' Dr Richardson says, spawning 'lifestyle' illnesses such as rheumatoid arthritis, allergies, diabetes and heart disease. Until the agrotech wizards perfect their hi-tech algebra, making 6s into 3s, eating more fish and less grain is the only choice we have.

· This article was amended on Thursday September 27 2007.