UK dividend income for non resident indvividuals is considered 'disregarded income'. SAIM1170 advises "A non-UK resident person is taxable on savings and investment income". It goes on to describe 'UK dividends and bank interest' as one of several sources of 'disregarded income'. Special rules apply to disregarded income, so that the non UK resident's income tax liability is limited to the "sum of tax deducted from, or treated as deducted from, or tax credits on ‘disregarded income’, and the tax liability leaving out the disregarded income and with no personal allowances or double taxation relief taken into account". What this is saying is, two calculations are required.
The first to work out how much tax was deducted or treated as deducted from, or tax credits tax credits on ‘disregarded income’ and the second to work out how much tax is chargeable following normal calculations process with no personal allowances, allowing personal saving allowances and starting rate for savings, as appropriate for the amount of income.
The lower figure of the two calculations is the amount of tax due. If you have paid more tax than the lower figure, a refund of the difference is due. If you have paid less tax than is calculated, the liability is limited to the tax already paid, so no additional tax liability and no refund due.
If your only sources of income in the UK is disregared income, then the £5000 starting rate for savings would apply and the personal savings allowance of £1000, £500 or £0, depending on the amount of disregarded income.
SAIM1170 - Savings and investment income: non-residents
Tax on savings interest