Unless you use a tax-efficient savings product like an ISA the interest added to your savings is taxable. Basic rate tax is taken off automatically by the provider so if you're a basic rate taxpayer you don't need to do anything.
If you're a higher-rate taxpayer, you must pay the additional tax through your self-assessment tax return.
If you don't pay any tax, you can apply to receive tax-free interest on your savings or claim back the tax you have already paid.