How interest and dividends are taxed on top of other income, what the Personal Savings Allowance, the starting rate for savings and the Dividend Allowance each do, and where ISAs and joint accounts change the answer.
Primary source: Income Tax rates and allowances (GOV.UK).
Savings interest and dividends are both income, but they are not taxed in the same way as wages. They are added on top of a taxpayer's other income and then taxed at their own rates, with their own nil-rate bands. The order matters: the bands are filled by non-savings income first, so the rate that applies to interest or dividends depends on how much other income there is.
Interest on savings is taxed as income, but a band of it is taxed at 0% through the Personal Savings Allowance. The size of the allowance depends on the taxpayer's marginal rate: a basic-rate taxpayer gets the largest band, a higher-rate taxpayer a smaller one, and an additional-rate taxpayer none at all. The allowance is a nil-rate band rather than an exemption, so interest within it still counts towards total income.
There is a separate 0% band for savings income for people whose other income is low. It applies to savings income only, and it is reduced pound for pound by non-savings income above the Personal Allowance. The starting rate and the Personal Savings Allowance can both apply to the same taxpayer, and the starting rate is used first.
Interest on a joint account is treated as belonging to each holder equally unless a different split reflects the actual ownership of the money. Each holder's share is taxed against their own allowance and bands, so a joint account can use two Personal Savings Allowances where a single account would use one.
An Individual Savings Account is exempt from Income Tax and Capital Gains Tax on the investments held inside it. Interest, dividends and gains within an ISA do not count towards the Personal Savings Allowance, the Dividend Allowance or the annual exempt amount, and they do not need to be reported on a tax return.
Dividends are taxed at their own rates, and a band of dividend income is taxed at 0% through the Dividend Allowance. Like the Personal Savings Allowance, it is a nil-rate band rather than an exemption: dividend income within it still counts towards total income and can still push other income into a higher band.
A director or shareholder who takes both a salary and dividends is taxed on the total. The salary uses the Personal Allowance and the bands first; dividends are then added on top and taxed at the dividend rates. A salary is also earnings for National Insurance, while a dividend is not.
A company pays Corporation Tax on its profits before dividends are paid, so a dividend is not a deductible expense. The shareholder then pays Income Tax on the dividend received. The two taxes are separate and are charged on different people — the company on its profits, the shareholder on the distribution.