http://www.moneysavingexpert.com/savings/child-savings-tax-free
There's a common myth that children don't pay tax - that's simply not true. In fact, they're taxed in exactly the same way as adults. Each child can, in the 2014-15 tax year, earn up to £10,000 tax-free from salary, savings or investments.
The difference is, unlike most adults, most children don't use up their allowance, so their savings interest is tax-free.
Assuming your child won't earn more than £10,000 (watch out child prodigies!), ensure any interest is paid without tax being automatically deducted by filling out the Inland Revenue's R85 form (the bank should give you one of these).
If you've already overpaid, you'll need to fill out an R40 form to get it back.