Since the government introduced the savings allowance the bank no longer deducts tax at source from your interest received.
Most individuals only receive minimal amounts of interest and it is likely no further tax would be due as this is covered by the interest allowance.
If you are receiving large amounts of interest it is really important that you ensure that you notify HMRC if tax is due on the amounts.
At time of writing if you are a basic rate tax payer you can receive interest of £1,000 tax free, if you are a higher rate tax payer its £500, an additional rate tax payer has no allowance. If you receive interest in excess of these amounts it must be declared to the revenue.