High expectations.

Watching a program about a contest called "Britain's brightest child" I was struck by the fact that none of the kids were white children. Of course in modern Britain I should not be asking this sort of question since there is a presumption in my question that race has an influence.

In some ways of course it does but not as measure of a child's ability, rather it is a measure of the parents willingness to encourage and become embroiled in their child's life particularly their educational attainment. These children had grown up surrounded by books and musical instruments and were encouraged to learn from them. Of course in some children this type of interaction can be stimulating whilst in others it creates a barrier and it's hard to judge which way it will turn out.
There is of course another way where the parent is obsessive about the child and their achievement whilst growing up and it is often in such a family that one sees the attainment of a skill, playing the piano, academic study, even the skills needed to play a sport are nurtured from an early age. Perhaps there's is an assumption amongst the white families who have gifted children that their normal progression in life is enough whilst Chinese and Indian parents know through experience that life's opportunities have to be grasped against fierce opposition and only by constant tutoring can the child be prepared to be one of the best.
It takes a special kind of parent who thinks ahead in this way.
Others set aside money to pay exorbitant school fees and the teacher becomes the surrogate parent whilst the child competes with his classmates but this is a far cry from a parent devoting all their time and money solely on the child to nurture the talent.
Of course it's obsessive and has drawbacks but even given the fragility that this goldfish bowl existence can do to the child's, what we would call normal social skills, the results can be mind boggling in the level of skill it extracts.
It begs the question, does this level of untapped skill lie within all of us ? Without the pummelling of this extreme parental discipline, we are but rough 'unfinished' objects of what we might have been ?