Many children have savings accounts in some form. If they were born between September 2002 and January 2011 they may had had a Child Trust Fund, a tax-free savings account set up by government, or perhaps its successor the Junior ISA.
Both of these entities enabled family and friends to help encourage children to save by contributing funds.
The new Personal Savings Allowance which applies for the current 2016/17 tax year together with the level of tax-free Personal Allowance available to all UK individuals enables children to accumulate income from various sources without having to suffer income tax.
Care must be taken however if parents are providing capital for a child's account. Children can only earn £100 a year interest from money given from each parent, step-parent or guardian. If they earn more, the whole of the interest is taxed at the parent's rate of tax. This doesn't apply to interest arising from money given to children by grandparents, other family or friends.
Creating family trusts for the benefit of children, their future education and wellbeing are not uncommon. Although these can be tax-efficient they need to be discussed with and written by specialist lawyers or accountants. If they are ineffective legally then there may be significant tax to pay by the person or persons settling the funds. Always take advice if you are contemplating this route.