Even randomly selecting from those countries, most would be ethnic Brit/French/etc, bar major population shifts between now and then. (I also suspect that the selection board for the new colony might favor farmers, who in my neck of the woods tend to be folks whose families have owned land for generations.) It would, of course, select people who aren't "lily white", which fits with the canon description of the average Barrayaran as being olive-skinned – darker than the average ethnic Briton, French, or Russian.

Ethnicity is a combination of phenotype, culture, and language. Sure, there are folks who fit the latter two but not the phenotype prototype and are described as Britons, but they typically get an adjective that modifies the noun. The prototypical ethnic Briton would be someone who doesn't get an adjective in front of the descriptor.