The State Pension is part of a pensioner’s taxable income. The problem is, it is paid gross, without deduction of tax.
If your sole source of income is the State Pension then this should cause no problem as the State Pension is usually below the annual tax-free personal allowance. What can, and does, cause a problem is if you have other sources of income that combined with your State Pension exceed your personal tax-free allowance.
The assumption most pensioners make is that they can spend their State Pension. Unfortunately, this can lead to cash flow problems if a tax bill drops through your door. This should only happen if you have other income sources and any tax stopped on those additional income streams is insufficient to cover your total tax liabilities: based on all your income including State Pension receipts.
If you have additional income and receive a State Pension, it is necessary to crunch the numbers and see if you should be saving to meet a future tax bill. Readers concerned about their position should talk to the tax office or their professional tax advisor.