As a matter of interest, there is a plan in America where contributions can be made tax free into an educational savings account. An individual can 'give away' up to $11k per year without incurring tax. Anyone who wants can contribute to a child's education fund (dh, dw, grandparents, etc.) The money grows tax free, and is not taxed when it is removed, as long as it is used for educational expenses.
Typically, it is expected that the plan will be used to fund University costs. Also, doesn't matter if the money is used for a state or private school.