Having a Personal Pension does not affect your entitlement to a state pension. Once you retire and your pensions (state and personal for instance) start to pay out to you they will be taxed jointly.

What this means is that once your State Pension is added to your Personal Pension you will be taxed at your income tax rate. 

For example the full state pension of £95.25 a week represents an annual income of £4953

If your personal pension provides an income of £20,000 a year your total taxable income would be £20,000 + 4953 = £24,953.