: UK Capital Gains tax and Income If a UK resident makes a capital gain of £25000 and has a state pension of £6000 are they liable for any UK tax, given that there is a capital gains allowance and a tax allowance?

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Depending on the tax year, the Capital Gains tax allowance is about £12,000 and the personal income tax allowance is about £12,500.

It looks like you can't count unused personal income tax allowance against capital gains:

Unused Income Tax reliefs and allowances cannot be set against the net gains.

So there'll be tax owing on about £13,000 - at a rate of 10%, or 18% if the gain is from residential property.

To calculate the exact tax, follow the steps listed at www.gov.uk/capital-gains-tax/rates:

Subtract the personal allowance (e.g. £12,500 for 2019-20) from your pension (£6,000). If this is a negative number, as in this case, treat it as 0.
Deduct the Capital Gains allowance (e.g. £12,000) from the gain (£25,000) to get £13,000.
Add it to your taxable income to check what tax band the result falls into. In this case you get £13,000 which is well within the basic rate band. You'll pay 10% or 18% tax on this amount.