This is an amazing result. I am almost reluctant to report it, though, because no one has a very good idea why it is true.
British researchers have been following a large group of babies born in the late 1930s into their 70s. There was not a big difference in class among breastfeeders in those days (as there is now, when breastfeeding is skewed toward the middle class). Yet breastfed babies were 41% more likely than other kids to move up a class, net of their initial class and family income. Breastfed kids were even 16% more likely to move up a class than their own bottlefed siblings.
One thing not reported in the press account: whether birth order and family size mattered. My best guess is that first-borns were more likely to be breastfed. This might explain the intra-sibling difference. First-borns would then be more likely to move up in class for a variety of reasons, not least because their parents wanted them to. It may also be that all the kids were more likely to be breastfed in smaller families. We know that later-born children in large families are more likely to have lower IQs and lower rates of upward mobility. If smaller families were more likely to breastfeed all the kids, and less likely to have low-achieving later-borns, this might account for the main finding.
Just a guess, though. Maybe La Leche League might want to invest in some research grants.