Babies who are fed on demand are more likely to have a higher IQ and perform better at school, according to new research.
The study suggests that eight-year-olds who were demand-fed as infants had IQs that were four or five points higher than those who were fed to a schedule.
Researchers from Essex and Oxford Universities looked at three types of mothers and babies - babies who were fed to a schedule, for example every four hours, when they were four weeks old, those whose mother tried but did not manage to feed to a schedule, and those who were fed on demand.
The data was drawn from the Avon Longitudinal Study of Parents and Children, a study of more than 10,000 children born in the Bristol area in the early 1990s.
The findings show that feeding on demand is associated with higher IQ scores at the age of eight, and better performance in national curriculum tests, known as Sats, at ages five, seven, 11 and 14.
This is after taking into account background factors such as a parent's education, family income, the child's sex and age, maternal health and parenting styles.
Mothers who fed to a schedule are more likely to be younger, single, social tenants and less educated, the study says.
Children with mothers who tried to feed to a schedule but did not manage it had similar Sats results and IQ scores as youngsters who were demand fed, the study found.
Dr Maria Iacovou from the Institute for Social and Economic Research at Essex University said: "The difference between schedule and demand-fed children is found both in breastfed and in bottle-fed babies.
"The difference in IQ levels of around four to five points, though statistically highly significant, would not make a child at the bottom of the class move to the top, but it would be noticeable."
She said that in a class of 30 children, a pupil who is right in the middle of the class, ranked at 15th, could be ranked at around 11th or 12th with an an improvement of four or five IQ points.
The study, published in the European Journal of Public Health, concludes that mothers whofed to a schedule were more likely to get more sleep and to get more enjoyment out of parenting.
But it adds: "There appears to be a trade-off: children who were fed to a schedule go on to do less well in attainment and IQ tests, at all ages from five to 14."
Dr Iacovou said that this was the first large-scale study of the long-term differences between feeding to a schedule and feeding on demand, and warned there must be caution about claiming a causal link between feeding patterns and IQ.
"This research is based on large-scale data and we are confident that there is a very low risk that the results arose by chance," she said.
"Nonetheless, this is the first and only study of its kind, and further research is needed before we can say categorically that how you feed your baby has a long-term impact on his or her IQ and academic attainment, and before we can say definitively what the mechanisms are by which this relationship comes about."