All interest you receive is taxable, unless it is from an ISA, but banks and building societies no longer deduct tax from interest paid to individuals. For most taxpayers the rate of tax payable on that interest is 0%, so no tax is in fact due.
This zero tax rate applies where your savings income falls within your Savings Rate Band (SRB), which is worth up to £5,000, or within your Personal Savings Allowance (PSA), which is worth £1,000 for basic rate taxpayers or £500 for higher rate taxpayers. Any savings income which falls outside the SRB or PSA is taxed at your marginal Income Tax rate (currently 20%, 40% or 45%).
The available SRB depends on how much other taxable non-savings income you receive, such as salary, pensions, trading profits or rent. If you can control the type of income you receive you can reduce the total tax you pay for the year.