This usually depends on the age of the child and how you've opened the account. Typically, if your child is under eight the account will be held in trust by the adult(s) who opened it. However, some accounts allow you to remain a signatory until your child is 16.
Many accounts have terms and conditions stating withdrawn money must be used "for the benefit of the child", but of course, this covers a wide variety of definitions.
Once your child is old enough, they will also be able to manage the account, either online, in branch and via ATMs – depending on the features the account offers. See our best-buy tables above to compare the best rates.