The research, based on two large groups of people born 12 years apart, shows that those who had been breastfed in both eras had similarly improved their chances of social mobility.
The study has been welcomed by campaigners who have long promoted the benefits of breastfeeding.
Lead researcher Professor Amanda Sacker, director at University College London’s Centre for Lifecourse Studies in Society and Health, said: “This information is important to all mothers with children, not only those who breastfeed.
“We don’t know if the link is the nutrients of the milk or the close, skin-to-skin contact and bonding between mother and child.
“So for mothers who are unable to breastfeed, or don’t want to breastfeed, there are still things they can do to possibly improve their children’s social mobility, such as increase their own social contact.”
The study suggests that those who are breastfed are likely to have a higher social class than their fathers by the time they reach their mid-thirties.
Researchers examined data from 17,400 children born in 1958 and 16,800 children born in 1970, who were followed up for about 50 years.
The study, published in the Archives of Disease in Childhood, compared people’s social class as children – based on the social class of their father when they were 10 or 11 – with their social class as adults, measured when they were 33 or 34.
The researchers found that more than two-thirds (68 per cent) of mothers breastfed their children in 1958, compared with just over a third (36 per cent) in 1970. Nonetheless, when background factors were accounted for, children who had been breastfed were consistently more likely to have climbed the social ladder than those who had not been breastfed.
Breastfeeding increased the odds of upwards mobility by 24 per cent and reduced the odds of downward mobility by around 20 per cent for both groups, the authors found.
Prof Sacker said: “The fact we found the same results in two separate groups, from different years, means we are more confident about our findings.
“Breastfeeding enhances brain development, which boosts intellect, which in turn increases upwards social mobility. Breastfed children also showed fewer signs of stress.
“The evidence suggests breastfeeding confers a range of long-term health, developmental and behavioural advantages, which persist into adulthood.”
But she pointed out that it was difficult to pinpoint which gave a child the greatest benefit – the nutrients in breast milk or the close contact and associated bonding during breastfeeding.
She said: “Perhaps the combination is implicated in the better neurocognitive and adult outcomes of breastfed infants.”
Karen MacKay, registered midwife and lactation consultant for NHS Highland, said: “There is a clear link that breastfeeding can break the divide between inequalities.
“We hope to raise the profile of the benefits of breastfeeding and reduce the impact of social inequality.”