Cultural psychologists have shown that people from Western, Educated, Industrialised, Rich, Democratic (WEIRD) countries often exhibit different psychological processing to people from less-WEIRD countries. The former exhibit more individualistic and less collectivistic social orientation, and more analytic and less holistic cognition, than non-Westerners. Yet the mechanisms responsible for maintaining this cultural variation are unclear. Immigration is an ideal 'natural experiment' for uncovering such mechanisms. We used a battery of psychological measures previously shown to vary cross-culturally to compare the social orientation and cognitive style of 286 residents of East London from three cultural backgrounds: (i) 1st-generation British Bangladeshi immigrants; (ii) 2nd-generation British Bangladeshis raised in the UK to Bangladeshi-raised parents; and (iii) non-migrants whose parents were born and raised in the UK. Model comparison revealed that individualism and dispositional attribution, typical of Western societies, are driven primarily by horizontal cultural transmission (e.g. via mass media), with parents and other family members having little or no effect, while collectivism, social closeness and situational attribution were driven by a mix of vertical/oblique cultural transmission (e.g. via family contact) and horizontal cultural transmission. These individual-level transmission dynamics can explain hitherto puzzling population-level phenomena, such as the partial acculturation of 2nd-generation immigrants on measures such as collectivism (due to the mix of vertical and horizontal cultural transmission), or the observation in several countries of increasing individualism (which is transmitted horizontally and therefore rapidly) despite little corresponding change in collectivism (which is transmitted partly vertically and therefore more slowly). Further consideration of cultural transmission mechanisms, in conjunction with the study of migrant communities and model comparison statistics, can shed light on the persistence of, and changes in, culturally-variable psychological processes.