A lot of people were opted out of SERPS without any choice. But having said that if you were opted out the slight reduction on your state pension is more than compensated for in the increased value of the company pension.
Income tax is payable on any income that exceeds the personal allowance which is around £12k.
When doing their sums HMRC always put the state pension first, which is just a bit below the allowance figure, so any other income, such as private pension, or part time job, is likely to be fully taxed.